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How to use it?
Least common denominator:
m^2-4/m^2+6*m+9*m+3/m-2
exp(x)/(2*sqrt(1-exp(2*x)/4))
exp(x)/2+exp(-x)/2
exp(x)/(1-x)+exp(x)/(1-x)^2
Factor polynomial:
x^3-x^2-x+20
x^3-x-2*x^2
x^3-x^2-3*x+27
x^3-x^2-3*x+2
Factor squared:
y^2+13*y*b-4*b^2
y^2-12*y*x+7*x^2
-y^2+10*y*x+x^2
y^2-11*y+1
How do you in partial fractions?:
(12*p+1)/(p^3+3*p^2+2*p+3)
atan(((2*sin(2*x))/(1+cos(2*x))+1)/sqrt(3))/sqrt(3)
(7-5*m)/(m-4)+4*m/(m+4)*(m*m-16)/(4*m)+(9*m-23)/(m-4)
((5*c-c^2)/(25*c^2-10*c+1)+4/(1-25*c^2)):(1-(3/(5c-1)))
Identical expressions
cos(x)^log(x)*(log(cos(x))/x-log(x)*sin(x)/cos(x))
co sinus of e of (x) to the power of logarithm of (x) multiply by ( logarithm of ( co sinus of e of (x)) divide by x minus logarithm of (x) multiply by sinus of (x) divide by co sinus of e of (x))
cos(x)log(x)*(log(cos(x))/x-log(x)*sin(x)/cos(x))
cosxlogx*logcosx/x-logx*sinx/cosx
cos(x)^log(x)(log(cos(x))/x-log(x)sin(x)/cos(x))
cos(x)log(x)(log(cos(x))/x-log(x)sin(x)/cos(x))
cosxlogxlogcosx/x-logxsinx/cosx
cosx^logxlogcosx/x-logxsinx/cosx
cos(x)^log(x)*(log(cos(x)) divide by x-log(x)*sin(x) divide by cos(x))
Similar expressions
cos(x)^log(x)*(log(cos(x))/x+log(x)*sin(x)/cos(x))
cosx^log(x)*(log(cosx)/x-log(x)*sinx/cosx)

Expression simplification/ Least common denominator/ cos(x)^log(x)*(log(cos(x))/x-log(x)*sin(x)/cos(x))

Least common denominator cos(x)^log(x)(log(cos(x))/x-log(x)sin(x)/cos(x))

The solution

You have entered [src]

   log(x)    /log(cos(x))   log(x)*sin(x)\
cos      (x)*|----------- - -------------|
             \     x            cos(x)   /

$$\left(- \frac{\log{\left(x \right)} \sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{\log{\left(\cos{\left(x \right)} \right)}}{x}\right) \cos^{\log{\left(x \right)}}{\left(x \right)}$$

cos(x)^log(x)*(log(cos(x))/x - log(x)*sin(x)/cos(x))

General simplification [src]

   -1 + log(x)                                          
cos           (x)*(cos(x)*log(cos(x)) - x*log(x)*sin(x))
--------------------------------------------------------
                           x

$$\frac{\left(- x \log{\left(x \right)} \sin{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)}\right) \cos^{\log{\left(x \right)} - 1}{\left(x \right)}}{x}$$

cos(x)^(-1 + log(x))*(cos(x)*log(cos(x)) - x*log(x)*sin(x))/x

Combinatorics [src]

    log(x)                                            
-cos      (x)*(-cos(x)*log(cos(x)) + x*log(x)*sin(x)) 
------------------------------------------------------
                       x*cos(x)

$$- \frac{\left(x \log{\left(x \right)} \sin{\left(x \right)} - \log{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)}\right) \cos^{\log{\left(x \right)}}{\left(x \right)}}{x \cos{\left(x \right)}}$$

-cos(x)^log(x)*(-cos(x)*log(cos(x)) + x*log(x)*sin(x))/(x*cos(x))

Rational denominator [src]

   log(x)                                          
cos      (x)*(cos(x)*log(cos(x)) - x*log(x)*sin(x))
---------------------------------------------------
                      x*cos(x)

$$\frac{\left(- x \log{\left(x \right)} \sin{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)}\right) \cos^{\log{\left(x \right)}}{\left(x \right)}}{x \cos{\left(x \right)}}$$

cos(x)^log(x)*(cos(x)*log(cos(x)) - x*log(x)*sin(x))/(x*cos(x))

Common denominator [src]

 /     log(x)                              log(x)                 \ 
-\- cos      (x)*cos(x)*log(cos(x)) + x*cos      (x)*log(x)*sin(x)/ 
--------------------------------------------------------------------
                              x*cos(x)

$$- \frac{x \log{\left(x \right)} \sin{\left(x \right)} \cos^{\log{\left(x \right)}}{\left(x \right)} - \log{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)} \cos^{\log{\left(x \right)}}{\left(x \right)}}{x \cos{\left(x \right)}}$$

-(-cos(x)^log(x)*cos(x)*log(cos(x)) + x*cos(x)^log(x)*log(x)*sin(x))/(x*cos(x))

Numerical answer [src]

cos(x)^log(x)*(log(cos(x))/x - log(x)*sin(x)/cos(x))

cos(x)^log(x)*(log(cos(x))/x - log(x)*sin(x)/cos(x))

Powers [src]

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

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

(exp(i*x)/2 + exp(-i*x)/2)^log(x)*(log(exp(i*x)/2 + exp(-i*x)/2)/x + i*(-exp(-i*x) + exp(i*x))*log(x)/(2*(exp(i*x)/2 + exp(-i*x)/2)))

Combining rational expressions [src]

   log(x)                                          
cos      (x)*(cos(x)*log(cos(x)) - x*log(x)*sin(x))
---------------------------------------------------
                      x*cos(x)

cos(x)^log(x)*(cos(x)*log(cos(x)) - x*log(x)*sin(x))/(x*cos(x))

Expand expression [src]

   log(x)                     log(x)                 
cos      (x)*log(cos(x))   cos      (x)*log(x)*sin(x)
------------------------ - --------------------------
           x                         cos(x)

$$- \frac{\log{\left(x \right)} \sin{\left(x \right)} \cos^{\log{\left(x \right)}}{\left(x \right)}}{\cos{\left(x \right)}} + \frac{\log{\left(\cos{\left(x \right)} \right)} \cos^{\log{\left(x \right)}}{\left(x \right)}}{x}$$

cos(x)^log(x)*log(cos(x))/x - cos(x)^log(x)*log(x)*sin(x)/cos(x)

Trigonometric part [src]

                  /   /   /    pi\\                   \
                  |log|sin|x + --||        2          |
   log(x)/    pi\ |   \   \    2 //   2*sin (x)*log(x)|
sin      |x + --|*|---------------- - ----------------|
         \    2 / \       x               sin(2*x)    /

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

   log(x)    /log(cos(x))                \
cos      (x)*|----------- - log(x)*tan(x)|
             \     x                     /

$$\left(- \log{\left(x \right)} \tan{\left(x \right)} + \frac{\log{\left(\cos{\left(x \right)} \right)}}{x}\right) \cos^{\log{\left(x \right)}}{\left(x \right)}$$

                    /   /       2/x\\                \
                    |   |1 - tan |-||                |
                    |   |        \2/|                |
             log(x) |log|-----------|                |
/       2/x\\       |   |       2/x\|                |
|1 - tan |-||       |   |1 + tan |-||                |
|        \2/|       |   \        \2//                |
|-----------|      *|---------------- - log(x)*tan(x)|
|       2/x\|       \       x                        /
|1 + tan |-||                                         
\        \2//

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

               /   /  1   \                \
        log(x) |log|------|                |
/  1   \       |   \sec(x)/   log(x)*sec(x)|
|------|      *|----------- - -------------|
\sec(x)/       |     x            /    pi\ |
               |               sec|x - --| |
               \                  \    2 / /

$$\left(- \frac{\log{\left(x \right)} \sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}} + \frac{\log{\left(\frac{1}{\sec{\left(x \right)}} \right)}}{x}\right) \left(\frac{1}{\sec{\left(x \right)}}\right)^{\log{\left(x \right)}}$$

               /   /  1   \                \
        log(x) |log|------|                |
/  1   \       |   \sec(x)/   log(x)*sec(x)|
|------|      *|----------- - -------------|
\sec(x)/       \     x            csc(x)   /

$$\left(- \frac{\log{\left(x \right)} \sec{\left(x \right)}}{\csc{\left(x \right)}} + \frac{\log{\left(\frac{1}{\sec{\left(x \right)}} \right)}}{x}\right) \left(\frac{1}{\sec{\left(x \right)}}\right)^{\log{\left(x \right)}}$$

                  /   /   /    pi\\                \
                  |log|sin|x + --||                |
   log(x)/    pi\ |   \   \    2 //   log(x)*sin(x)|
sin      |x + --|*|---------------- - -------------|
         \    2 / |       x               /    pi\ |
                  |                    sin|x + --| |
                  \                       \    2 / /

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

                     /   /        2/x\\                  \
                     |   |-1 + cot |-||                  |
                     |   |         \2/|                  |
              log(x) |log|------------|                  |
/        2/x\\       |   |       2/x\ |        /x\       |
|-1 + cot |-||       |   |1 + cot |-| |   2*cot|-|*log(x)|
|         \2/|       |   \        \2/ /        \2/       |
|------------|      *|----------------- - ---------------|
|       2/x\ |       |        x                     2/x\ |
|1 + cot |-| |       |                      -1 + cot |-| |
\        \2/ /       \                               \2/ /

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

                     /   /        2/x\\         \
                     |   |-1 + cot |-||         |
                     |   |         \2/|         |
              log(x) |log|------------|         |
/        2/x\\       |   |       2/x\ |         |
|-1 + cot |-||       |   |1 + cot |-| |         |
|         \2/|       |   \        \2/ /   log(x)|
|------------|      *|----------------- - ------|
|       2/x\ |       \        x           cot(x)/
|1 + cot |-| |                                   
\        \2/ /

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

                    /   /       2/x\\                  \
                    |   |1 - tan |-||                  |
                    |   |        \2/|                  |
             log(x) |log|-----------|                  |
/       2/x\\       |   |       2/x\|               /x\|
|1 - tan |-||       |   |1 + tan |-||   2*log(x)*tan|-||
|        \2/|       |   \        \2//               \2/|
|-----------|      *|---------------- - ---------------|
|       2/x\|       |       x                    2/x\  |
|1 + tan |-||       |                     1 - tan |-|  |
\        \2//       \                             \2/  /

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

             /                 /    pi\       \
             |              cos|x - --|*log(x)|
   log(x)    |log(cos(x))      \    2 /       |
cos      (x)*|----------- - ------------------|
             \     x              cos(x)      /

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

                    /   /     1     \                     \
                    |log|-----------|                     |
                    |   |   /pi    \|      /pi    \       |
             log(x) |   |csc|-- - x||   csc|-- - x|*log(x)|
/     1     \       |   \   \2     //      \2     /       |
|-----------|      *|---------------- - ------------------|
|   /pi    \|       \       x                 csc(x)      /
|csc|-- - x||                                              
\   \2     //

$$\left(- \frac{\log{\left(x \right)} \csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}} + \frac{\log{\left(\frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}} \right)}}{x}\right) \left(\frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right)^{\log{\left(x \right)}}$$

(1/csc(pi/2 - x))^log(x)*(log(1/csc(pi/2 - x))/x - csc(pi/2 - x)*log(x)/csc(x))

Other calculators

How to use it?

Identical expressions

Similar expressions

Least common denominator cos(x)^log(x)*(log(cos(x))/x-log(x)*sin(x)/cos(x))

The solution

Least common denominator cos(x)^log(x)(log(cos(x))/x-log(x)sin(x)/cos(x))