Mister Exam

Lang:

Other calculators

How to use it?
Least common denominator:
exp(x/2)/sqrt(1-exp(x))-exp(-x)/(2*sqrt(exp(-x)-1))
(((exp(1)-1)^3*log(e))/3)-((6*(exp(1)-1)-3*(exp(1)-1)^2+2*(exp(1)-1)^3)/18)
cot(x)^(atan(x)+1)*(log(cot(x))/(1+x^2)+(-1-cot(x)^2)*(atan(x)+1)/cot(x))
cot(x)^2*(-3-3*cot(x)^2)/tan(x)^2-cot(x)^3*(2+2*tan(x)^2)/tan(x)^3
Factor polynomial:
x^3+8*x^2-6*x-48
x^3-7*x^2+15*x
x^3+6*x*y+3*y^2-18*x-18*y
x^3+6*x^2*y+12*x*y^2+8*y^3
Factor squared:
-x^4+x^2-3
x^4-9*x^2+7
-x^4+9*x^2-5
-x^4+9*x^2+5
How do you in partial fractions?:
a-1/(3*a^2+6*a+3)-1/(2*a+2)
-2/(x-1)^2
(2tgx)/(1+tg^2x)
(2+sqrt(4+t)/sqrt(t+4))/(2-sqrt(t+4))
Identical expressions
cot(x)^ two *(- three - three *cot(x)^ two)/tan(x)^ two -cot(x)^ three *(two + two *tan(x)^ two)/tan(x)^ three
cotangent of (x) squared multiply by ( minus 3 minus 3 multiply by cotangent of (x) squared ) divide by tangent of (x) squared minus cotangent of (x) cubed multiply by (2 plus 2 multiply by tangent of (x) squared ) divide by tangent of (x) cubed
cotangent of (x) to the power of two multiply by ( minus three minus three multiply by cotangent of (x) to the power of two) divide by tangent of (x) to the power of two minus cotangent of (x) to the power of three multiply by (two plus two multiply by tangent of (x) to the power of two) divide by tangent of (x) to the power of three
cot(x)2*(-3-3*cot(x)2)/tan(x)2-cot(x)3*(2+2*tan(x)2)/tan(x)3
cotx2*-3-3*cotx2/tanx2-cotx3*2+2*tanx2/tanx3
cot(x)²*(-3-3*cot(x)²)/tan(x)²-cot(x)³*(2+2*tan(x)²)/tan(x)³
cot(x) to the power of 2*(-3-3*cot(x) to the power of 2)/tan(x) to the power of 2-cot(x) to the power of 3*(2+2*tan(x) to the power of 2)/tan(x) to the power of 3
cot(x)^2(-3-3cot(x)^2)/tan(x)^2-cot(x)^3(2+2tan(x)^2)/tan(x)^3
cot(x)2(-3-3cot(x)2)/tan(x)2-cot(x)3(2+2tan(x)2)/tan(x)3
cotx2-3-3cotx2/tanx2-cotx32+2tanx2/tanx3
cotx^2-3-3cotx^2/tanx^2-cotx^32+2tanx^2/tanx^3
cot(x)^2*(-3-3*cot(x)^2) divide by tan(x)^2-cot(x)^3*(2+2*tan(x)^2) divide by tan(x)^3
Similar expressions
cot(x)^2*(-3-3*cot(x)^2)/tan(x)^2-cot(x)^3*(2-2*tan(x)^2)/tan(x)^3
cot(x)^2*(3-3*cot(x)^2)/tan(x)^2-cot(x)^3*(2+2*tan(x)^2)/tan(x)^3
cot(x)^2*(-3-3*cot(x)^2)/tan(x)^2+cot(x)^3*(2+2*tan(x)^2)/tan(x)^3
cot(x)^2*(-3+3*cot(x)^2)/tan(x)^2-cot(x)^3*(2+2*tan(x)^2)/tan(x)^3

Expression simplification/ Least common denominator/ cot(x)^2*(-3-3*cot(x)^2)/tan(x)^2-cot(x)^3*(2+2*tan(x)^2)/tan(x)^3

Least common denominator cot(x)^2(-3-3cot(x)^2)/tan(x)^2-cot(x)^3(2+2tan(x)^2)/tan(x)^3

The solution

You have entered [src]

   2    /          2   \      3    /         2   \
cot (x)*\-3 - 3*cot (x)/   cot (x)*\2 + 2*tan (x)/
------------------------ - -----------------------
           2                          3           
        tan (x)                    tan (x)

$$- \frac{\left(2 \tan^{2}{\left(x \right)} + 2\right) \cot^{3}{\left(x \right)}}{\tan^{3}{\left(x \right)}} + \frac{\left(- 3 \cot^{2}{\left(x \right)} - 3\right) \cot^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)}}$$

(cot(x)^2*(-3 - 3*cot(x)^2))/tan(x)^2 - cot(x)^3*(2 + 2*tan(x)^2)/tan(x)^3

General simplification [src]

      -10       
----------------
            5   
sin(2*x)*tan (x)

$$- \frac{10}{\sin{\left(2 x \right)} \tan^{5}{\left(x \right)}}$$

-10/(sin(2*x)*tan(x)^5)

Combining rational expressions [src]

   2    /    /       2   \            /        2   \       \
cot (x)*\- 2*\1 + tan (x)/*cot(x) + 3*\-1 - cot (x)/*tan(x)/
------------------------------------------------------------
                             3                              
                          tan (x)

$$\frac{\left(- 2 \left(\tan^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} + 3 \left(- \cot^{2}{\left(x \right)} - 1\right) \tan{\left(x \right)}\right) \cot^{2}{\left(x \right)}}{\tan^{3}{\left(x \right)}}$$

cot(x)^2*(-2*(1 + tan(x)^2)*cot(x) + 3*(-1 - cot(x)^2)*tan(x))/tan(x)^3

Powers [src]

                                                                       /                      2\
                                                             3         |      /   I*x    -I*x\ |
                                               / I*x    -I*x\     3    |    2*\- e    + e    / |
                                             I*\e    + e    / *cot (x)*|2 - -------------------|
                2                                                      |                    2  |
  / I*x    -I*x\     2    /          2   \                             |      / I*x    -I*x\   |
  \e    + e    / *cot (x)*\-3 - 3*cot (x)/                             \      \e    + e    /   /
- ---------------------------------------- - ---------------------------------------------------
                             2                                                3                 
             /   I*x    -I*x\                                 /   I*x    -I*x\                  
             \- e    + e    /                                 \- e    + e    /

$$- \frac{i \left(- \frac{2 \left(- e^{i x} + e^{- i x}\right)^{2}}{\left(e^{i x} + e^{- i x}\right)^{2}} + 2\right) \left(e^{i x} + e^{- i x}\right)^{3} \cot^{3}{\left(x \right)}}{\left(- e^{i x} + e^{- i x}\right)^{3}} - \frac{\left(e^{i x} + e^{- i x}\right)^{2} \left(- 3 \cot^{2}{\left(x \right)} - 3\right) \cot^{2}{\left(x \right)}}{\left(- e^{i x} + e^{- i x}\right)^{2}}$$

   2    /          2   \      3    /          2   \
cot (x)*\-3 - 3*cot (x)/   cot (x)*\-2 - 2*tan (x)/
------------------------ + ------------------------
           2                          3            
        tan (x)                    tan (x)

$$\frac{\left(- 2 \tan^{2}{\left(x \right)} - 2\right) \cot^{3}{\left(x \right)}}{\tan^{3}{\left(x \right)}} + \frac{\left(- 3 \cot^{2}{\left(x \right)} - 3\right) \cot^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)}}$$

cot(x)^2*(-3 - 3*cot(x)^2)/tan(x)^2 + cot(x)^3*(-2 - 2*tan(x)^2)/tan(x)^3

Rational denominator [src]

   2       3    /          2   \      3       2    /         2   \
cot (x)*tan (x)*\-3 - 3*cot (x)/ - cot (x)*tan (x)*\2 + 2*tan (x)/
------------------------------------------------------------------
                                5                                 
                             tan (x)

$$\frac{- \left(2 \tan^{2}{\left(x \right)} + 2\right) \tan^{2}{\left(x \right)} \cot^{3}{\left(x \right)} + \left(- 3 \cot^{2}{\left(x \right)} - 3\right) \tan^{3}{\left(x \right)} \cot^{2}{\left(x \right)}}{\tan^{5}{\left(x \right)}}$$

(cot(x)^2*tan(x)^3*(-3 - 3*cot(x)^2) - cot(x)^3*tan(x)^2*(2 + 2*tan(x)^2))/tan(x)^5

Numerical answer [src]

cot(x)^2*(-3.0 - 3.0*cot(x)^2)/tan(x)^2 - cot(x)^3*(2.0 + 2.0*tan(x)^2)/tan(x)^3

cot(x)^2*(-3.0 - 3.0*cot(x)^2)/tan(x)^2 - cot(x)^3*(2.0 + 2.0*tan(x)^2)/tan(x)^3

Common denominator [src]

 /     3           3       2           2                  4          \ 
-\2*cot (x) + 2*cot (x)*tan (x) + 3*cot (x)*tan(x) + 3*cot (x)*tan(x)/ 
-----------------------------------------------------------------------
                                   3                                   
                                tan (x)

$$- \frac{2 \tan^{2}{\left(x \right)} \cot^{3}{\left(x \right)} + 3 \tan{\left(x \right)} \cot^{4}{\left(x \right)} + 3 \tan{\left(x \right)} \cot^{2}{\left(x \right)} + 2 \cot^{3}{\left(x \right)}}{\tan^{3}{\left(x \right)}}$$

-(2*cot(x)^3 + 2*cot(x)^3*tan(x)^2 + 3*cot(x)^2*tan(x) + 3*cot(x)^4*tan(x))/tan(x)^3

Combinatorics [src]

    2    /                           2                  2          \ 
-cot (x)*\2*cot(x) + 3*tan(x) + 2*tan (x)*cot(x) + 3*cot (x)*tan(x)/ 
---------------------------------------------------------------------
                                  3                                  
                               tan (x)

$$- \frac{\left(2 \tan^{2}{\left(x \right)} \cot{\left(x \right)} + 3 \tan{\left(x \right)} \cot^{2}{\left(x \right)} + 3 \tan{\left(x \right)} + 2 \cot{\left(x \right)}\right) \cot^{2}{\left(x \right)}}{\tan^{3}{\left(x \right)}}$$

-cot(x)^2*(2*cot(x) + 3*tan(x) + 2*tan(x)^2*cot(x) + 3*cot(x)^2*tan(x))/tan(x)^3

Expand expression [src]

       2           4           3           3   
  3*cot (x)   3*cot (x)   2*cot (x)   2*cot (x)
- --------- - --------- - --------- - ---------
      2           2         tan(x)        3    
   tan (x)     tan (x)                 tan (x)

$$- \frac{2 \cot^{3}{\left(x \right)}}{\tan{\left(x \right)}} - \frac{3 \cot^{4}{\left(x \right)}}{\tan^{2}{\left(x \right)}} - \frac{3 \cot^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)}} - \frac{2 \cot^{3}{\left(x \right)}}{\tan^{3}{\left(x \right)}}$$

-3*cot(x)^2/tan(x)^2 - 3*cot(x)^4/tan(x)^2 - 2*cot(x)^3/tan(x) - 2*cot(x)^3/tan(x)^3

Trigonometric part [src]

       4    
 -5*cos (x) 
------------
   6/    pi\
cos |x - --|
    \    2 /

$$- \frac{5 \cos^{4}{\left(x \right)}}{\cos^{6}{\left(x - \frac{\pi}{2} \right)}}$$

        3                   
-3 - -------                
        2               2   
     tan (x)   2 + 2*tan (x)
------------ - -------------
     4               6      
  tan (x)         tan (x)

$$\frac{-3 - \frac{3}{\tan^{2}{\left(x \right)}}}{\tan^{4}{\left(x \right)}} - \frac{2 \tan^{2}{\left(x \right)} + 2}{\tan^{6}{\left(x \right)}}$$

      4/    pi\
-5*sin |x + --|
       \    2 /
---------------
       6       
    sin (x)

$$- \frac{5 \sin^{4}{\left(x + \frac{\pi}{2} \right)}}{\sin^{6}{\left(x \right)}}$$

   4    /          2   \      6    /       2   \
cot (x)*\-3 - 3*cot (x)/ - cot (x)*|2 + -------|
                                   |       2   |
                                   \    cot (x)/

$$- \left(2 + \frac{2}{\cot^{2}{\left(x \right)}}\right) \cot^{6}{\left(x \right)} + \left(- 3 \cot^{2}{\left(x \right)} - 3\right) \cot^{4}{\left(x \right)}$$

             /          2/    pi\\                /          2     \
             |     3*sec |x - --||      6/    pi\ |     2*sec (x)  |
   4/    pi\ |           \    2 /|   sec |x - --|*|2 + ------------|
sec |x - --|*|-3 - --------------|       \    2 / |       2/    pi\|
    \    2 / |           2       |                |    sec |x - --||
             \        sec (x)    /                \        \    2 //
---------------------------------- - -------------------------------
                4                                   6               
             sec (x)                             sec (x)

$$\frac{\left(-3 - \frac{3 \sec^{2}{\left(x - \frac{\pi}{2} \right)}}{\sec^{2}{\left(x \right)}}\right) \sec^{4}{\left(x - \frac{\pi}{2} \right)}}{\sec^{4}{\left(x \right)}} - \frac{\left(\frac{2 \sec^{2}{\left(x \right)}}{\sec^{2}{\left(x - \frac{\pi}{2} \right)}} + 2\right) \sec^{6}{\left(x - \frac{\pi}{2} \right)}}{\sec^{6}{\left(x \right)}}$$

            /         4   \             /          2     \
     6      |    8*sin (x)|      4      |     3*sin (2*x)|
  sin (2*x)*|2 + ---------|   sin (2*x)*|-3 - -----------|
            |       2     |             |           4    |
            \    sin (2*x)/             \      4*sin (x) /
- ------------------------- + ----------------------------
               12                            8            
         64*sin  (x)                   16*sin (x)

$$\frac{\left(-3 - \frac{3 \sin^{2}{\left(2 x \right)}}{4 \sin^{4}{\left(x \right)}}\right) \sin^{4}{\left(2 x \right)}}{16 \sin^{8}{\left(x \right)}} - \frac{\left(\frac{8 \sin^{4}{\left(x \right)}}{\sin^{2}{\left(2 x \right)}} + 2\right) \sin^{6}{\left(2 x \right)}}{64 \sin^{12}{\left(x \right)}}$$

                2               4
   /       2/x\\  /        2/x\\ 
-5*|1 + cot |-|| *|-1 + cot |-|| 
   \        \2//  \         \2// 
---------------------------------
                  6/x\           
            64*cot |-|           
                   \2/

$$- \frac{5 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{4} \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}{64 \cot^{6}{\left(\frac{x}{2} \right)}}$$

        /          2   \           /         2   \
   4    |     3*csc (x)|      6    |    2*sec (x)|
csc (x)*|-3 - ---------|   csc (x)*|2 + ---------|
        |         2    |           |        2    |
        \      sec (x) /           \     csc (x) /
------------------------ - -----------------------
           4                          6           
        sec (x)                    sec (x)

$$- \frac{\left(2 + \frac{2 \sec^{2}{\left(x \right)}}{\csc^{2}{\left(x \right)}}\right) \csc^{6}{\left(x \right)}}{\sec^{6}{\left(x \right)}} + \frac{\left(- \frac{3 \csc^{2}{\left(x \right)}}{\sec^{2}{\left(x \right)}} - 3\right) \csc^{4}{\left(x \right)}}{\sec^{4}{\left(x \right)}}$$

        /           2     \           /         2/    pi\\
   4    |      3*cos (x)  |           |    2*cos |x - --||
cos (x)*|-3 - ------------|      6    |          \    2 /|
        |        2/    pi\|   cos (x)*|2 + --------------|
        |     cos |x - --||           |          2       |
        \         \    2 //           \       cos (x)    /
--------------------------- - ----------------------------
           4/    pi\                     6/    pi\        
        cos |x - --|                  cos |x - --|        
            \    2 /                      \    2 /

$$- \frac{\left(2 + \frac{2 \cos^{2}{\left(x - \frac{\pi}{2} \right)}}{\cos^{2}{\left(x \right)}}\right) \cos^{6}{\left(x \right)}}{\cos^{6}{\left(x - \frac{\pi}{2} \right)}} + \frac{\left(- \frac{3 \cos^{2}{\left(x \right)}}{\cos^{2}{\left(x - \frac{\pi}{2} \right)}} - 3\right) \cos^{4}{\left(x \right)}}{\cos^{4}{\left(x - \frac{\pi}{2} \right)}}$$

      4       6   
-5*cos (x)*csc (x)

$$- 5 \cos^{4}{\left(x \right)} \csc^{6}{\left(x \right)}$$

        /          2   \           /         2   \
   4    |     3*cos (x)|      6    |    2*sin (x)|
cos (x)*|-3 - ---------|   cos (x)*|2 + ---------|
        |         2    |           |        2    |
        \      sin (x) /           \     cos (x) /
------------------------ - -----------------------
           4                          6           
        sin (x)                    sin (x)

$$\frac{\left(-3 - \frac{3 \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \cos^{4}{\left(x \right)}}{\sin^{4}{\left(x \right)}} - \frac{\left(\frac{2 \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 2\right) \cos^{6}{\left(x \right)}}{\sin^{6}{\left(x \right)}}$$

       6    
 -5*csc (x) 
------------
   4/pi    \
csc |-- - x|
    \2     /

$$- \frac{5 \csc^{6}{\left(x \right)}}{\csc^{4}{\left(- x + \frac{\pi}{2} \right)}}$$

                4 
   /       2/x\\  
-5*|1 - tan |-||  
   \        \2//  
------------------
      4/x\    6/x\
64*cos |-|*tan |-|
       \2/     \2/

$$- \frac{5 \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{4}}{64 \cos^{4}{\left(\frac{x}{2} \right)} \tan^{6}{\left(\frac{x}{2} \right)}}$$

      4   
-5*cos (x)
----------
    6     
 sin (x)

$$- \frac{5 \cos^{4}{\left(x \right)}}{\sin^{6}{\left(x \right)}}$$

                 4        
   /        2/x\\     6/x\
-5*|-1 + cot |-|| *tan |-|
   \         \2//      \2/
--------------------------
              4/x\        
        64*sin |-|        
               \2/

$$- \frac{5 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{4} \tan^{6}{\left(\frac{x}{2} \right)}}{64 \sin^{4}{\left(\frac{x}{2} \right)}}$$

      6/    pi\
-5*sec |x - --|
       \    2 /
---------------
       4       
    sec (x)

$$- \frac{5 \sec^{6}{\left(x - \frac{\pi}{2} \right)}}{\sec^{4}{\left(x \right)}}$$

        /           2     \           /         2/pi    \\
   4    |      3*csc (x)  |           |    2*csc |-- - x||
csc (x)*|-3 - ------------|      6    |          \2     /|
        |        2/pi    \|   csc (x)*|2 + --------------|
        |     csc |-- - x||           |          2       |
        \         \2     //           \       csc (x)    /
--------------------------- - ----------------------------
           4/pi    \                     6/pi    \        
        csc |-- - x|                  csc |-- - x|        
            \2     /                      \2     /

$$- \frac{\left(2 + \frac{2 \csc^{2}{\left(- x + \frac{\pi}{2} \right)}}{\csc^{2}{\left(x \right)}}\right) \csc^{6}{\left(x \right)}}{\csc^{6}{\left(- x + \frac{\pi}{2} \right)}} + \frac{\left(- \frac{3 \csc^{2}{\left(x \right)}}{\csc^{2}{\left(- x + \frac{\pi}{2} \right)}} - 3\right) \csc^{4}{\left(x \right)}}{\csc^{4}{\left(- x + \frac{\pi}{2} \right)}}$$

                2              4
   /       2/x\\  /       2/x\\ 
-5*|1 + tan |-|| *|1 - tan |-|| 
   \        \2//  \        \2// 
--------------------------------
                 6/x\           
           64*tan |-|           
                  \2/

$$- \frac{5 \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{4} \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}{64 \tan^{6}{\left(\frac{x}{2} \right)}}$$

-5*(1 + tan(x/2)^2)^2*(1 - tan(x/2)^2)^4/(64*tan(x/2)^6)

Other calculators

How to use it?

Identical expressions

Similar expressions

Least common denominator cot(x)^2*(-3-3*cot(x)^2)/tan(x)^2-cot(x)^3*(2+2*tan(x)^2)/tan(x)^3

The solution

Least common denominator cot(x)^2(-3-3cot(x)^2)/tan(x)^2-cot(x)^3(2+2tan(x)^2)/tan(x)^3