Mister Exam

Other calculators

ysin²xlny+y=0 equation

The teacher will be very surprised to see your correct solution 😉

v

Numerical solution:

Do search numerical solution at [, ]

The solution

You have entered [src] 
     2                  
y*sin (x)*log(y) + y = 0
y+ysin⁡2(x)log⁡(y)=0y + y \sin^{2}{\left(x \right)} \log{\left(y \right)} = 0
Simplify
Detail solution
Given the equation
y+ysin⁡2(x)log⁡(y)=0y + y \sin^{2}{\left(x \right)} \log{\left(y \right)} = 0
transform
ylog⁡(y)sin⁡2(x)+y−1=0y \log{\left(y \right)} \sin^{2}{\left(x \right)} + y - 1 = 0
y+ysin⁡2(x)log⁡(y)−1=0y + y \sin^{2}{\left(x \right)} \log{\left(y \right)} - 1 = 0
Do replacement
w=sin⁡(x)w = \sin{\left(x \right)}
This equation is of the form
a*w^2 + b*w + c = 0

A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
w1=D−b2aw_{1} = \frac{\sqrt{D} - b}{2 a}
w2=−D−b2aw_{2} = \frac{- \sqrt{D} - b}{2 a}
where D = b^2 - 4*a*c - it is the discriminant.
Because
a=ylog⁡(y)a = y \log{\left(y \right)}
b=0b = 0
c=y−1c = y - 1
, then
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (y*log(y)) * (-1 + y) = -4*y*(-1 + y)*log(y)

The equation has two roots.
w1 = (-b + sqrt(D)) / (2*a)

w2 = (-b - sqrt(D)) / (2*a)

or
w1=−y(y−1)log⁡(y)ylog⁡(y)w_{1} = \frac{\sqrt{- y \left(y - 1\right) \log{\left(y \right)}}}{y \log{\left(y \right)}}
w2=−−y(y−1)log⁡(y)ylog⁡(y)w_{2} = - \frac{\sqrt{- y \left(y - 1\right) \log{\left(y \right)}}}{y \log{\left(y \right)}}
do backward replacement
sin⁡(x)=w\sin{\left(x \right)} = w
substitute w:
The graph
Rapid solution [src] 
                                                                                                                                                                 2            2                                                                                               2           2                                                                                                 2            2                                                                                               2           2                                                                                                                                                              
                                                                                                                                                              cos (re(x))*sinh (im(x))                                                                                    cosh (im(x))*sin (re(x))                                                                                       cos (re(x))*sinh (im(x))                                                                                    cosh (im(x))*sin (re(x))                                                                                                                                                       
                                                                                                                     --------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------      --------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------                                                                                                               
                                                                                                                        4            4              4           4               2            2           2            2             4            4              4           4               2            2           2            2                4            4              4           4               2            2           2            2             4            4              4           4               2            2           2            2                                                                                                                      
        /                             2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x))                             \  cos (re(x))*sinh (im(x)) + cosh (im(x))*sin (re(x)) + 2*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x))   cos (re(x))*sinh (im(x)) + cosh (im(x))*sin (re(x)) + 2*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x))      cos (re(x))*sinh (im(x)) + cosh (im(x))*sin (re(x)) + 2*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x))   cos (re(x))*sinh (im(x)) + cosh (im(x))*sin (re(x)) + 2*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x))    /                             2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x))                             \
y1 = cos|---------------------------------------------------------------------------------------------------------|*e                                                                                                                                                                                                                      + I*e                                                                                                                                                                                                                     *sin|---------------------------------------------------------------------------------------------------------|
        |   4            4              4           4               2            2           2            2       |                                                                                                                                                                                                                                                                                                                                                                                                                                                      |   4            4              4           4               2            2           2            2       |
        \cos (re(x))*sinh (im(x)) + cosh (im(x))*sin (re(x)) + 2*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x))/                                                                                                                                                                                                                                                                                                                                                                                                                                                      \cos (re(x))*sinh (im(x)) + cosh (im(x))*sin (re(x)) + 2*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x))/
y1=ie−sin⁡2(re⁡(x))cosh⁡2(im⁡(x))sin⁡4(re⁡(x))cosh⁡4(im⁡(x))+2sin⁡2(re⁡(x))cos⁡2(re⁡(x))sinh⁡2(im⁡(x))cosh⁡2(im⁡(x))+cos⁡4(re⁡(x))sinh⁡4(im⁡(x))+cos⁡2(re⁡(x))sinh⁡2(im⁡(x))sin⁡4(re⁡(x))cosh⁡4(im⁡(x))+2sin⁡2(re⁡(x))cos⁡2(re⁡(x))sinh⁡2(im⁡(x))cosh⁡2(im⁡(x))+cos⁡4(re⁡(x))sinh⁡4(im⁡(x))sin⁡(2sin⁡(re⁡(x))cos⁡(re⁡(x))sinh⁡(im⁡(x))cosh⁡(im⁡(x))sin⁡4(re⁡(x))cosh⁡4(im⁡(x))+2sin⁡2(re⁡(x))cos⁡2(re⁡(x))sinh⁡2(im⁡(x))cosh⁡2(im⁡(x))+cos⁡4(re⁡(x))sinh⁡4(im⁡(x)))+e−sin⁡2(re⁡(x))cosh⁡2(im⁡(x))sin⁡4(re⁡(x))cosh⁡4(im⁡(x))+2sin⁡2(re⁡(x))cos⁡2(re⁡(x))sinh⁡2(im⁡(x))cosh⁡2(im⁡(x))+cos⁡4(re⁡(x))sinh⁡4(im⁡(x))+cos⁡2(re⁡(x))sinh⁡2(im⁡(x))sin⁡4(re⁡(x))cosh⁡4(im⁡(x))+2sin⁡2(re⁡(x))cos⁡2(re⁡(x))sinh⁡2(im⁡(x))cosh⁡2(im⁡(x))+cos⁡4(re⁡(x))sinh⁡4(im⁡(x))cos⁡(2sin⁡(re⁡(x))cos⁡(re⁡(x))sinh⁡(im⁡(x))cosh⁡(im⁡(x))sin⁡4(re⁡(x))cosh⁡4(im⁡(x))+2sin⁡2(re⁡(x))cos⁡2(re⁡(x))sinh⁡2(im⁡(x))cosh⁡2(im⁡(x))+cos⁡4(re⁡(x))sinh⁡4(im⁡(x)))y_{1} = i e^{- \frac{\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}}{\sin^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{4}{\left(\operatorname{im}{\left(x\right)} \right)} + 2 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{4}{\left(\operatorname{im}{\left(x\right)} \right)}} + \frac{\cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}}{\sin^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{4}{\left(\operatorname{im}{\left(x\right)} \right)} + 2 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{4}{\left(\operatorname{im}{\left(x\right)} \right)}}} \sin{\left(\frac{2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}}{\sin^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{4}{\left(\operatorname{im}{\left(x\right)} \right)} + 2 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{4}{\left(\operatorname{im}{\left(x\right)} \right)}} \right)} + e^{- \frac{\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}}{\sin^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{4}{\left(\operatorname{im}{\left(x\right)} \right)} + 2 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{4}{\left(\operatorname{im}{\left(x\right)} \right)}} + \frac{\cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}}{\sin^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{4}{\left(\operatorname{im}{\left(x\right)} \right)} + 2 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{4}{\left(\operatorname{im}{\left(x\right)} \right)}}} \cos{\left(\frac{2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}}{\sin^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{4}{\left(\operatorname{im}{\left(x\right)} \right)} + 2 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{4}{\left(\operatorname{im}{\left(x\right)} \right)}} \right)} 
y1 = i*exp(-sin(re(x))^2*cosh(im(x))^2/(sin(re(x))^4*cosh(im(x))^4 + 2*sin(re(x))^2*cos(re(x))^2*sinh(im(x))^2*cosh(im(x))^2 + cos(re(x))^4*sinh(im(x))^4) + cos(re(x))^2*sinh(im(x))^2/(sin(re(x))^4*cosh(im(x))^4 + 2*sin(re(x))^2*cos(re(x))^2*sinh(im(x))^2*cosh(im(x))^2 + cos(re(x))^4*sinh(im(x))^4))*sin(2*sin(re(x))*cos(re(x))*sinh(im(x))*cosh(im(x))/(sin(re(x))^4*cosh(im(x))^4 + 2*sin(re(x))^2*cos(re(x))^2*sinh(im(x))^2*cosh(im(x))^2 + cos(re(x))^4*sinh(im(x))^4)) + exp(-sin(re(x))^2*cosh(im(x))^2/(sin(re(x))^4*cosh(im(x))^4 + 2*sin(re(x))^2*cos(re(x))^2*sinh(im(x))^2*cosh(im(x))^2 + cos(re(x))^4*sinh(im(x))^4) + cos(re(x))^2*sinh(im(x))^2/(sin(re(x))^4*cosh(im(x))^4 + 2*sin(re(x))^2*cos(re(x))^2*sinh(im(x))^2*cosh(im(x))^2 + cos(re(x))^4*sinh(im(x))^4))*cos(2*sin(re(x))*cos(re(x))*sinh(im(x))*cosh(im(x))/(sin(re(x))^4*cosh(im(x))^4 + 2*sin(re(x))^2*cos(re(x))^2*sinh(im(x))^2*cosh(im(x))^2 + cos(re(x))^4*sinh(im(x))^4))
Sum and product of roots [src] 
sum
                                                                                                                                                            2            2                                                                                               2           2                                                                                                 2            2                                                                                               2           2                                                                                                                                                              
                                                                                                                                                         cos (re(x))*sinh (im(x))                                                                                    cosh (im(x))*sin (re(x))                                                                                       cos (re(x))*sinh (im(x))                                                                                    cosh (im(x))*sin (re(x))                                                                                                                                                       
                                                                                                                --------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------      --------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------                                                                                                               
                                                                                                                   4            4              4           4               2            2           2            2             4            4              4           4               2            2           2            2                4            4              4           4               2            2           2            2             4            4              4           4               2            2           2            2                                                                                                                      
   /                             2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x))                             \  cos (re(x))*sinh (im(x)) + cosh (im(x))*sin (re(x)) + 2*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x))   cos (re(x))*sinh (im(x)) + cosh (im(x))*sin (re(x)) + 2*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x))      cos (re(x))*sinh (im(x)) + cosh (im(x))*sin (re(x)) + 2*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x))   cos (re(x))*sinh (im(x)) + cosh (im(x))*sin (re(x)) + 2*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x))    /                             2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x))                             \
cos|---------------------------------------------------------------------------------------------------------|*e                                                                                                                                                                                                                      + I*e                                                                                                                                                                                                                     *sin|---------------------------------------------------------------------------------------------------------|
   |   4            4              4           4               2            2           2            2       |                                                                                                                                                                                                                                                                                                                                                                                                                                                      |   4            4              4           4               2            2           2            2       |
   \cos (re(x))*sinh (im(x)) + cosh (im(x))*sin (re(x)) + 2*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x))/                                                                                                                                                                                                                                                                                                                                                                                                                                                      \cos (re(x))*sinh (im(x)) + cosh (im(x))*sin (re(x)) + 2*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x))/
ie−sin⁡2(re⁡(x))cosh⁡2(im⁡(x))sin⁡4(re⁡(x))cosh⁡4(im⁡(x))+2sin⁡2(re⁡(x))cos⁡2(re⁡(x))sinh⁡2(im⁡(x))cosh⁡2(im⁡(x))+cos⁡4(re⁡(x))sinh⁡4(im⁡(x))+cos⁡2(re⁡(x))sinh⁡2(im⁡(x))sin⁡4(re⁡(x))cosh⁡4(im⁡(x))+2sin⁡2(re⁡(x))cos⁡2(re⁡(x))sinh⁡2(im⁡(x))cosh⁡2(im⁡(x))+cos⁡4(re⁡(x))sinh⁡4(im⁡(x))sin⁡(2sin⁡(re⁡(x))cos⁡(re⁡(x))sinh⁡(im⁡(x))cosh⁡(im⁡(x))sin⁡4(re⁡(x))cosh⁡4(im⁡(x))+2sin⁡2(re⁡(x))cos⁡2(re⁡(x))sinh⁡2(im⁡(x))cosh⁡2(im⁡(x))+cos⁡4(re⁡(x))sinh⁡4(im⁡(x)))+e−sin⁡2(re⁡(x))cosh⁡2(im⁡(x))sin⁡4(re⁡(x))cosh⁡4(im⁡(x))+2sin⁡2(re⁡(x))cos⁡2(re⁡(x))sinh⁡2(im⁡(x))cosh⁡2(im⁡(x))+cos⁡4(re⁡(x))sinh⁡4(im⁡(x))+cos⁡2(re⁡(x))sinh⁡2(im⁡(x))sin⁡4(re⁡(x))cosh⁡4(im⁡(x))+2sin⁡2(re⁡(x))cos⁡2(re⁡(x))sinh⁡2(im⁡(x))cosh⁡2(im⁡(x))+cos⁡4(re⁡(x))sinh⁡4(im⁡(x))cos⁡(2sin⁡(re⁡(x))cos⁡(re⁡(x))sinh⁡(im⁡(x))cosh⁡(im⁡(x))sin⁡4(re⁡(x))cosh⁡4(im⁡(x))+2sin⁡2(re⁡(x))cos⁡2(re⁡(x))sinh⁡2(im⁡(x))cosh⁡2(im⁡(x))+cos⁡4(re⁡(x))sinh⁡4(im⁡(x)))i e^{- \frac{\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}}{\sin^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{4}{\left(\operatorname{im}{\left(x\right)} \right)} + 2 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{4}{\left(\operatorname{im}{\left(x\right)} \right)}} + \frac{\cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}}{\sin^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{4}{\left(\operatorname{im}{\left(x\right)} \right)} + 2 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{4}{\left(\operatorname{im}{\left(x\right)} \right)}}} \sin{\left(\frac{2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}}{\sin^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{4}{\left(\operatorname{im}{\left(x\right)} \right)} + 2 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{4}{\left(\operatorname{im}{\left(x\right)} \right)}} \right)} + e^{- \frac{\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}}{\sin^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{4}{\left(\operatorname{im}{\left(x\right)} \right)} + 2 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{4}{\left(\operatorname{im}{\left(x\right)} \right)}} + \frac{\cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}}{\sin^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{4}{\left(\operatorname{im}{\left(x\right)} \right)} + 2 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{4}{\left(\operatorname{im}{\left(x\right)} \right)}}} \cos{\left(\frac{2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}}{\sin^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{4}{\left(\operatorname{im}{\left(x\right)} \right)} + 2 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{4}{\left(\operatorname{im}{\left(x\right)} \right)}} \right)} 
=
                                                                                                                                                            2            2                                                                                               2           2                                                                                                 2            2                                                                                               2           2                                                                                                                                                              
                                                                                                                                                         cos (re(x))*sinh (im(x))                                                                                    cosh (im(x))*sin (re(x))                                                                                       cos (re(x))*sinh (im(x))                                                                                    cosh (im(x))*sin (re(x))                                                                                                                                                       
                                                                                                                --------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------      --------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------                                                                                                               
                                                                                                                   4            4              4           4               2            2           2            2             4            4              4           4               2            2           2            2                4            4              4           4               2            2           2            2             4            4              4           4               2            2           2            2                                                                                                                      
   /                             2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x))                             \  cos (re(x))*sinh (im(x)) + cosh (im(x))*sin (re(x)) + 2*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x))   cos (re(x))*sinh (im(x)) + cosh (im(x))*sin (re(x)) + 2*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x))      cos (re(x))*sinh (im(x)) + cosh (im(x))*sin (re(x)) + 2*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x))   cos (re(x))*sinh (im(x)) + cosh (im(x))*sin (re(x)) + 2*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x))    /                             2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x))                             \
cos|---------------------------------------------------------------------------------------------------------|*e                                                                                                                                                                                                                      + I*e                                                                                                                                                                                                                     *sin|---------------------------------------------------------------------------------------------------------|
   |   4            4              4           4               2            2           2            2       |                                                                                                                                                                                                                                                                                                                                                                                                                                                      |   4            4              4           4               2            2           2            2       |
   \cos (re(x))*sinh (im(x)) + cosh (im(x))*sin (re(x)) + 2*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x))/                                                                                                                                                                                                                                                                                                                                                                                                                                                      \cos (re(x))*sinh (im(x)) + cosh (im(x))*sin (re(x)) + 2*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x))/
ie−sin⁡2(re⁡(x))cosh⁡2(im⁡(x))sin⁡4(re⁡(x))cosh⁡4(im⁡(x))+2sin⁡2(re⁡(x))cos⁡2(re⁡(x))sinh⁡2(im⁡(x))cosh⁡2(im⁡(x))+cos⁡4(re⁡(x))sinh⁡4(im⁡(x))+cos⁡2(re⁡(x))sinh⁡2(im⁡(x))sin⁡4(re⁡(x))cosh⁡4(im⁡(x))+2sin⁡2(re⁡(x))cos⁡2(re⁡(x))sinh⁡2(im⁡(x))cosh⁡2(im⁡(x))+cos⁡4(re⁡(x))sinh⁡4(im⁡(x))sin⁡(2sin⁡(re⁡(x))cos⁡(re⁡(x))sinh⁡(im⁡(x))cosh⁡(im⁡(x))sin⁡4(re⁡(x))cosh⁡4(im⁡(x))+2sin⁡2(re⁡(x))cos⁡2(re⁡(x))sinh⁡2(im⁡(x))cosh⁡2(im⁡(x))+cos⁡4(re⁡(x))sinh⁡4(im⁡(x)))+e−sin⁡2(re⁡(x))cosh⁡2(im⁡(x))sin⁡4(re⁡(x))cosh⁡4(im⁡(x))+2sin⁡2(re⁡(x))cos⁡2(re⁡(x))sinh⁡2(im⁡(x))cosh⁡2(im⁡(x))+cos⁡4(re⁡(x))sinh⁡4(im⁡(x))+cos⁡2(re⁡(x))sinh⁡2(im⁡(x))sin⁡4(re⁡(x))cosh⁡4(im⁡(x))+2sin⁡2(re⁡(x))cos⁡2(re⁡(x))sinh⁡2(im⁡(x))cosh⁡2(im⁡(x))+cos⁡4(re⁡(x))sinh⁡4(im⁡(x))cos⁡(2sin⁡(re⁡(x))cos⁡(re⁡(x))sinh⁡(im⁡(x))cosh⁡(im⁡(x))sin⁡4(re⁡(x))cosh⁡4(im⁡(x))+2sin⁡2(re⁡(x))cos⁡2(re⁡(x))sinh⁡2(im⁡(x))cosh⁡2(im⁡(x))+cos⁡4(re⁡(x))sinh⁡4(im⁡(x)))i e^{- \frac{\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}}{\sin^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{4}{\left(\operatorname{im}{\left(x\right)} \right)} + 2 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{4}{\left(\operatorname{im}{\left(x\right)} \right)}} + \frac{\cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}}{\sin^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{4}{\left(\operatorname{im}{\left(x\right)} \right)} + 2 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{4}{\left(\operatorname{im}{\left(x\right)} \right)}}} \sin{\left(\frac{2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}}{\sin^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{4}{\left(\operatorname{im}{\left(x\right)} \right)} + 2 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{4}{\left(\operatorname{im}{\left(x\right)} \right)}} \right)} + e^{- \frac{\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}}{\sin^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{4}{\left(\operatorname{im}{\left(x\right)} \right)} + 2 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{4}{\left(\operatorname{im}{\left(x\right)} \right)}} + \frac{\cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}}{\sin^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{4}{\left(\operatorname{im}{\left(x\right)} \right)} + 2 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{4}{\left(\operatorname{im}{\left(x\right)} \right)}}} \cos{\left(\frac{2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}}{\sin^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{4}{\left(\operatorname{im}{\left(x\right)} \right)} + 2 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{4}{\left(\operatorname{im}{\left(x\right)} \right)}} \right)} 
product
                                                                                                                                                            2            2                                                                                               2           2                                                                                                 2            2                                                                                               2           2                                                                                                                                                              
                                                                                                                                                         cos (re(x))*sinh (im(x))                                                                                    cosh (im(x))*sin (re(x))                                                                                       cos (re(x))*sinh (im(x))                                                                                    cosh (im(x))*sin (re(x))                                                                                                                                                       
                                                                                                                --------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------      --------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------                                                                                                               
                                                                                                                   4            4              4           4               2            2           2            2             4            4              4           4               2            2           2            2                4            4              4           4               2            2           2            2             4            4              4           4               2            2           2            2                                                                                                                      
   /                             2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x))                             \  cos (re(x))*sinh (im(x)) + cosh (im(x))*sin (re(x)) + 2*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x))   cos (re(x))*sinh (im(x)) + cosh (im(x))*sin (re(x)) + 2*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x))      cos (re(x))*sinh (im(x)) + cosh (im(x))*sin (re(x)) + 2*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x))   cos (re(x))*sinh (im(x)) + cosh (im(x))*sin (re(x)) + 2*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x))    /                             2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x))                             \
cos|---------------------------------------------------------------------------------------------------------|*e                                                                                                                                                                                                                      + I*e                                                                                                                                                                                                                     *sin|---------------------------------------------------------------------------------------------------------|
   |   4            4              4           4               2            2           2            2       |                                                                                                                                                                                                                                                                                                                                                                                                                                                      |   4            4              4           4               2            2           2            2       |
   \cos (re(x))*sinh (im(x)) + cosh (im(x))*sin (re(x)) + 2*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x))/                                                                                                                                                                                                                                                                                                                                                                                                                                                      \cos (re(x))*sinh (im(x)) + cosh (im(x))*sin (re(x)) + 2*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x))/
ie−sin⁡2(re⁡(x))cosh⁡2(im⁡(x))sin⁡4(re⁡(x))cosh⁡4(im⁡(x))+2sin⁡2(re⁡(x))cos⁡2(re⁡(x))sinh⁡2(im⁡(x))cosh⁡2(im⁡(x))+cos⁡4(re⁡(x))sinh⁡4(im⁡(x))+cos⁡2(re⁡(x))sinh⁡2(im⁡(x))sin⁡4(re⁡(x))cosh⁡4(im⁡(x))+2sin⁡2(re⁡(x))cos⁡2(re⁡(x))sinh⁡2(im⁡(x))cosh⁡2(im⁡(x))+cos⁡4(re⁡(x))sinh⁡4(im⁡(x))sin⁡(2sin⁡(re⁡(x))cos⁡(re⁡(x))sinh⁡(im⁡(x))cosh⁡(im⁡(x))sin⁡4(re⁡(x))cosh⁡4(im⁡(x))+2sin⁡2(re⁡(x))cos⁡2(re⁡(x))sinh⁡2(im⁡(x))cosh⁡2(im⁡(x))+cos⁡4(re⁡(x))sinh⁡4(im⁡(x)))+e−sin⁡2(re⁡(x))cosh⁡2(im⁡(x))sin⁡4(re⁡(x))cosh⁡4(im⁡(x))+2sin⁡2(re⁡(x))cos⁡2(re⁡(x))sinh⁡2(im⁡(x))cosh⁡2(im⁡(x))+cos⁡4(re⁡(x))sinh⁡4(im⁡(x))+cos⁡2(re⁡(x))sinh⁡2(im⁡(x))sin⁡4(re⁡(x))cosh⁡4(im⁡(x))+2sin⁡2(re⁡(x))cos⁡2(re⁡(x))sinh⁡2(im⁡(x))cosh⁡2(im⁡(x))+cos⁡4(re⁡(x))sinh⁡4(im⁡(x))cos⁡(2sin⁡(re⁡(x))cos⁡(re⁡(x))sinh⁡(im⁡(x))cosh⁡(im⁡(x))sin⁡4(re⁡(x))cosh⁡4(im⁡(x))+2sin⁡2(re⁡(x))cos⁡2(re⁡(x))sinh⁡2(im⁡(x))cosh⁡2(im⁡(x))+cos⁡4(re⁡(x))sinh⁡4(im⁡(x)))i e^{- \frac{\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}}{\sin^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{4}{\left(\operatorname{im}{\left(x\right)} \right)} + 2 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{4}{\left(\operatorname{im}{\left(x\right)} \right)}} + \frac{\cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}}{\sin^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{4}{\left(\operatorname{im}{\left(x\right)} \right)} + 2 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{4}{\left(\operatorname{im}{\left(x\right)} \right)}}} \sin{\left(\frac{2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}}{\sin^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{4}{\left(\operatorname{im}{\left(x\right)} \right)} + 2 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{4}{\left(\operatorname{im}{\left(x\right)} \right)}} \right)} + e^{- \frac{\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}}{\sin^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{4}{\left(\operatorname{im}{\left(x\right)} \right)} + 2 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{4}{\left(\operatorname{im}{\left(x\right)} \right)}} + \frac{\cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}}{\sin^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{4}{\left(\operatorname{im}{\left(x\right)} \right)} + 2 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{4}{\left(\operatorname{im}{\left(x\right)} \right)}}} \cos{\left(\frac{2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}}{\sin^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{4}{\left(\operatorname{im}{\left(x\right)} \right)} + 2 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{4}{\left(\operatorname{im}{\left(x\right)} \right)}} \right)} 
=
                                                                                           /    2           2             2            2       \        
                                                                                          -\cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))/        
                                                                                   ---------------------------------------------------------------------
                                                                                                                                                       2
                                                                                   /    2              2           2             2            2       \ 
/     /  2*sin(2*re(x))*sinh(2*im(x))  \      /  2*sin(2*re(x))*sinh(2*im(x))  \\  \sinh (im(x)) + cosh (im(x))*sin (re(x)) - sin (re(x))*sinh (im(x))/ 
|I*sin|--------------------------------| + cos|--------------------------------||*e                                                                     
|     |                               2|      |                               2||                                                                       
\     \(-cosh(2*im(x)) + cos(2*re(x))) /      \(-cosh(2*im(x)) + cos(2*re(x))) //
(isin⁡(2sin⁡(2re⁡(x))sinh⁡(2im⁡(x))(cos⁡(2re⁡(x))−cosh⁡(2im⁡(x)))2)+cos⁡(2sin⁡(2re⁡(x))sinh⁡(2im⁡(x))(cos⁡(2re⁡(x))−cosh⁡(2im⁡(x)))2))e−sin⁡2(re⁡(x))cosh⁡2(im⁡(x))−cos⁡2(re⁡(x))sinh⁡2(im⁡(x))(−sin⁡2(re⁡(x))sinh⁡2(im⁡(x))+sin⁡2(re⁡(x))cosh⁡2(im⁡(x))+sinh⁡2(im⁡(x)))2\left(i \sin{\left(\frac{2 \sin{\left(2 \operatorname{re}{\left(x\right)} \right)} \sinh{\left(2 \operatorname{im}{\left(x\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(x\right)} \right)} - \cosh{\left(2 \operatorname{im}{\left(x\right)} \right)}\right)^{2}} \right)} + \cos{\left(\frac{2 \sin{\left(2 \operatorname{re}{\left(x\right)} \right)} \sinh{\left(2 \operatorname{im}{\left(x\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(x\right)} \right)} - \cosh{\left(2 \operatorname{im}{\left(x\right)} \right)}\right)^{2}} \right)}\right) e^{- \frac{\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}}{\left(- \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}}} 
(i*sin(2*sin(2*re(x))*sinh(2*im(x))/(-cosh(2*im(x)) + cos(2*re(x)))^2) + cos(2*sin(2*re(x))*sinh(2*im(x))/(-cosh(2*im(x)) + cos(2*re(x)))^2))*exp(-(cosh(im(x))^2*sin(re(x))^2 - cos(re(x))^2*sinh(im(x))^2)/(sinh(im(x))^2 + cosh(im(x))^2*sin(re(x))^2 - sin(re(x))^2*sinh(im(x))^2)^2)
    © Mister Exam – Calculator