Sr Examen

Otras calculadoras

Simplificación de expresiones/ Descomposición en fracciones simples/ cos(x)^acot(x)*(-log(cos(x))/(1+x^2)-acot(x)*sin(x)/cos(x))

¿Cómo vas a descomponer esta cos(x)^acot(x)*(-log(cos(x))/(1+x^2)-acot(x)*sin(x)/cos(x)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   acot(x)    /-log(cos(x))    acot(x)*sin(x)\
cos       (x)*|------------- - --------------|
              |         2          cos(x)    |
              \    1 + x                     /
(−sin⁡(x)acot⁡(x)cos⁡(x)+(−1)log⁡(cos⁡(x))x2+1)cos⁡acot⁡(x)(x)\left(- \frac{\sin{\left(x \right)} \operatorname{acot}{\left(x \right)}}{\cos{\left(x \right)}} + \frac{\left(-1\right) \log{\left(\cos{\left(x \right)} \right)}}{x^{2} + 1}\right) \cos^{\operatorname{acot}{\left(x \right)}}{\left(x \right)} 
cos(x)^acot(x)*((-log(cos(x)))/(1 + x^2) - acot(x)*sin(x)/cos(x))
Simplificación general [src] 
    -1 + acot(x)    /                     /     2\               \ 
-cos            (x)*\cos(x)*log(cos(x)) + \1 + x /*acot(x)*sin(x)/ 
-------------------------------------------------------------------
                                    2                              
                               1 + x
−((x2+1)sin⁡(x)acot⁡(x)+log⁡(cos⁡(x))cos⁡(x))cos⁡acot⁡(x)−1(x)x2+1- \frac{\left(\left(x^{2} + 1\right) \sin{\left(x \right)} \operatorname{acot}{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)}\right) \cos^{\operatorname{acot}{\left(x \right)} - 1}{\left(x \right)}}{x^{2} + 1} 
-cos(x)^(-1 + acot(x))*(cos(x)*log(cos(x)) + (1 + x^2)*acot(x)*sin(x))/(1 + x^2)
Potencias [src] 
   acot(x)    /  log(cos(x))   acot(x)*sin(x)\
cos       (x)*|- ----------- - --------------|
              |          2         cos(x)    |
              \     1 + x                    /
(−sin⁡(x)acot⁡(x)cos⁡(x)−log⁡(cos⁡(x))x2+1)cos⁡acot⁡(x)(x)\left(- \frac{\sin{\left(x \right)} \operatorname{acot}{\left(x \right)}}{\cos{\left(x \right)}} - \frac{\log{\left(\cos{\left(x \right)} \right)}}{x^{2} + 1}\right) \cos^{\operatorname{acot}{\left(x \right)}}{\left(x \right)} 
                      /     / I*x    -I*x\                             \
              acot(x) |     |e      e    |                             |
/ I*x    -I*x\        |  log|---- + -----|     /   -I*x    I*x\        |
|e      e    |        |     \ 2       2  /   I*\- e     + e   /*acot(x)|
|---- + -----|       *|- ----------------- + --------------------------|
\ 2       2  /        |             2               / I*x    -I*x\     |
                      |        1 + x                |e      e    |     |
                      |                           2*|---- + -----|     |
                      \                             \ 2       2  /     /
(i(eix−e−ix)acot⁡(x)2(eix2+e−ix2)−log⁡(eix2+e−ix2)x2+1)(eix2+e−ix2)acot⁡(x)\left(\frac{i \left(e^{i x} - e^{- i x}\right) \operatorname{acot}{\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^{2} + 1}\right) \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{\operatorname{acot}{\left(x \right)}} 
(exp(i*x)/2 + exp(-i*x)/2)^acot(x)*(-log(exp(i*x)/2 + exp(-i*x)/2)/(1 + x^2) + i*(-exp(-i*x) + exp(i*x))*acot(x)/(2*(exp(i*x)/2 + exp(-i*x)/2)))
Denominador común [src] 
 /   acot(x)                        acot(x)                          2    acot(x)                  \ 
-\cos       (x)*acot(x)*sin(x) + cos       (x)*cos(x)*log(cos(x)) + x *cos       (x)*acot(x)*sin(x)/ 
-----------------------------------------------------------------------------------------------------
                                           2                                                         
                                          x *cos(x) + cos(x)
−x2sin⁡(x)cos⁡acot⁡(x)(x)acot⁡(x)+log⁡(cos⁡(x))cos⁡(x)cos⁡acot⁡(x)(x)+sin⁡(x)cos⁡acot⁡(x)(x)acot⁡(x)x2cos⁡(x)+cos⁡(x)- \frac{x^{2} \sin{\left(x \right)} \cos^{\operatorname{acot}{\left(x \right)}}{\left(x \right)} \operatorname{acot}{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)} \cos^{\operatorname{acot}{\left(x \right)}}{\left(x \right)} + \sin{\left(x \right)} \cos^{\operatorname{acot}{\left(x \right)}}{\left(x \right)} \operatorname{acot}{\left(x \right)}}{x^{2} \cos{\left(x \right)} + \cos{\left(x \right)}} 
-(cos(x)^acot(x)*acot(x)*sin(x) + cos(x)^acot(x)*cos(x)*log(cos(x)) + x^2*cos(x)^acot(x)*acot(x)*sin(x))/(x^2*cos(x) + cos(x))
Denominador racional [src] 
   acot(x)    /                      /     2\               \
cos       (x)*\-cos(x)*log(cos(x)) - \1 + x /*acot(x)*sin(x)/
-------------------------------------------------------------
                       /     2\                              
                       \1 + x /*cos(x)
(−(x2+1)sin⁡(x)acot⁡(x)−log⁡(cos⁡(x))cos⁡(x))cos⁡acot⁡(x)(x)(x2+1)cos⁡(x)\frac{\left(- \left(x^{2} + 1\right) \sin{\left(x \right)} \operatorname{acot}{\left(x \right)} - \log{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)}\right) \cos^{\operatorname{acot}{\left(x \right)}}{\left(x \right)}}{\left(x^{2} + 1\right) \cos{\left(x \right)}} 
cos(x)^acot(x)*(-cos(x)*log(cos(x)) - (1 + x^2)*acot(x)*sin(x))/((1 + x^2)*cos(x))
Abrimos la expresión [src] 
     acot(x)                     acot(x)                  
  cos       (x)*log(cos(x))   cos       (x)*acot(x)*sin(x)
- ------------------------- - ----------------------------
                 2                       cos(x)           
            1 + x
−sin⁡(x)cos⁡acot⁡(x)(x)acot⁡(x)cos⁡(x)−log⁡(cos⁡(x))cos⁡acot⁡(x)(x)x2+1- \frac{\sin{\left(x \right)} \cos^{\operatorname{acot}{\left(x \right)}}{\left(x \right)} \operatorname{acot}{\left(x \right)}}{\cos{\left(x \right)}} - \frac{\log{\left(\cos{\left(x \right)} \right)} \cos^{\operatorname{acot}{\left(x \right)}}{\left(x \right)}}{x^{2} + 1} 
-cos(x)^acot(x)*log(cos(x))/(1 + x^2) - cos(x)^acot(x)*acot(x)*sin(x)/cos(x)
Compilar la expresión [src] 
   acot(x)    /  log(cos(x))   acot(x)*sin(x)\
cos       (x)*|- ----------- - --------------|
              |          2         cos(x)    |
              \     1 + x                    /
(−sin⁡(x)acot⁡(x)cos⁡(x)−log⁡(cos⁡(x))x2+1)cos⁡acot⁡(x)(x)\left(- \frac{\sin{\left(x \right)} \operatorname{acot}{\left(x \right)}}{\cos{\left(x \right)}} - \frac{\log{\left(\cos{\left(x \right)} \right)}}{x^{2} + 1}\right) \cos^{\operatorname{acot}{\left(x \right)}}{\left(x \right)} 
cos(x)^acot(x)*(-log(cos(x))/(1 + x^2) - acot(x)*sin(x)/cos(x))
Unión de expresiones racionales [src] 
   acot(x)    /                      /     2\               \
cos       (x)*\-cos(x)*log(cos(x)) - \1 + x /*acot(x)*sin(x)/
-------------------------------------------------------------
                       /     2\                              
                       \1 + x /*cos(x)
(−(x2+1)sin⁡(x)acot⁡(x)−log⁡(cos⁡(x))cos⁡(x))cos⁡acot⁡(x)(x)(x2+1)cos⁡(x)\frac{\left(- \left(x^{2} + 1\right) \sin{\left(x \right)} \operatorname{acot}{\left(x \right)} - \log{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)}\right) \cos^{\operatorname{acot}{\left(x \right)}}{\left(x \right)}}{\left(x^{2} + 1\right) \cos{\left(x \right)}} 
cos(x)^acot(x)*(-cos(x)*log(cos(x)) - (1 + x^2)*acot(x)*sin(x))/((1 + x^2)*cos(x))
Parte trigonométrica [src] 
   acot(x)    /  log(cos(x))                 \
cos       (x)*|- ----------- - acot(x)*tan(x)|
              |          2                   |
              \     1 + x                    /
(−tan⁡(x)acot⁡(x)−log⁡(cos⁡(x))x2+1)cos⁡acot⁡(x)(x)\left(- \tan{\left(x \right)} \operatorname{acot}{\left(x \right)} - \frac{\log{\left(\cos{\left(x \right)} \right)}}{x^{2} + 1}\right) \cos^{\operatorname{acot}{\left(x \right)}}{\left(x \right)} 
                     /     /     1     \                      \
                     |  log|-----------|                      |
                     |     |   /pi    \|              /pi    \|
             acot(x) |     |csc|-- - x||   acot(x)*csc|-- - x||
/     1     \        |     \   \2     //              \2     /|
|-----------|       *|- ---------------- - -------------------|
|   /pi    \|        |            2               csc(x)      |
|csc|-- - x||        \       1 + x                            /
\   \2     //
(−acot⁡(x)csc⁡(−x+π2)csc⁡(x)−log⁡(1csc⁡(−x+π2))x2+1)(1csc⁡(−x+π2))acot⁡(x)\left(- \frac{\operatorname{acot}{\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^{2} + 1}\right) \left(\frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right)^{\operatorname{acot}{\left(x \right)}} 
                     /     /       2/x\\                   \
                     |     |1 - tan |-||                   |
                     |     |        \2/|                   |
             acot(x) |  log|-----------|                   |
/       2/x\\        |     |       2/x\|                /x\|
|1 - tan |-||        |     |1 + tan |-||   2*acot(x)*tan|-||
|        \2/|        |     \        \2//                \2/|
|-----------|       *|- ---------------- - ----------------|
|       2/x\|        |            2                 2/x\   |
|1 + tan |-||        |       1 + x           1 - tan |-|   |
\        \2//        \                               \2/   /
(1−tan⁡2(x2)tan⁡2(x2)+1)acot⁡(x)(−log⁡(1−tan⁡2(x2)tan⁡2(x2)+1)x2+1−2tan⁡(x2)acot⁡(x)1−tan⁡2(x2))\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{\operatorname{acot}{\left(x \right)}} \left(- \frac{\log{\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} \right)}}{x^{2} + 1} - \frac{2 \tan{\left(\frac{x}{2} \right)} \operatorname{acot}{\left(x \right)}}{1 - \tan^{2}{\left(\frac{x}{2} \right)}}\right) 
                      /     /        2/x\\                   \
                      |     |-1 + cot |-||                   |
                      |     |         \2/|                   |
              acot(x) |  log|------------|                   |
/        2/x\\        |     |       2/x\ |                /x\|
|-1 + cot |-||        |     |1 + cot |-| |   2*acot(x)*cot|-||
|         \2/|        |     \        \2/ /                \2/|
|------------|       *|- ----------------- - ----------------|
|       2/x\ |        |             2                  2/x\  |
|1 + cot |-| |        |        1 + x           -1 + cot |-|  |
\        \2/ /        \                                 \2/  /
(cot⁡2(x2)−1cot⁡2(x2)+1)acot⁡(x)(−2cot⁡(x2)acot⁡(x)cot⁡2(x2)−1−log⁡(cot⁡2(x2)−1cot⁡2(x2)+1)x2+1)\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{\operatorname{acot}{\left(x \right)}} \left(- \frac{2 \cot{\left(\frac{x}{2} \right)} \operatorname{acot}{\left(x \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^{2} + 1}\right) 
                     /     /       2/x\\                 \
                     |     |1 - tan |-||                 |
                     |     |        \2/|                 |
             acot(x) |  log|-----------|                 |
/       2/x\\        |     |       2/x\|                 |
|1 - tan |-||        |     |1 + tan |-||                 |
|        \2/|        |     \        \2//                 |
|-----------|       *|- ---------------- - acot(x)*tan(x)|
|       2/x\|        |            2                      |
|1 + tan |-||        \       1 + x                       /
\        \2//
(1−tan⁡2(x2)tan⁡2(x2)+1)acot⁡(x)(−tan⁡(x)acot⁡(x)−log⁡(1−tan⁡2(x2)tan⁡2(x2)+1)x2+1)\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{\operatorname{acot}{\left(x \right)}} \left(- \tan{\left(x \right)} \operatorname{acot}{\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^{2} + 1}\right) 
                      /     /        2/x\\          \
                      |     |-1 + cot |-||          |
                      |     |         \2/|          |
              acot(x) |  log|------------|          |
/        2/x\\        |     |       2/x\ |          |
|-1 + cot |-||        |     |1 + cot |-| |          |
|         \2/|        |     \        \2/ /   acot(x)|
|------------|       *|- ----------------- - -------|
|       2/x\ |        |             2         cot(x)|
|1 + cot |-| |        \        1 + x                /
\        \2/ /
(cot⁡2(x2)−1cot⁡2(x2)+1)acot⁡(x)(−acot⁡(x)cot⁡(x)−log⁡(cot⁡2(x2)−1cot⁡2(x2)+1)x2+1)\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{\operatorname{acot}{\left(x \right)}} \left(- \frac{\operatorname{acot}{\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^{2} + 1}\right) 
                   /     /   /    pi\\                 \
                   |  log|sin|x + --||                 |
   acot(x)/    pi\ |     \   \    2 //   acot(x)*sin(x)|
sin       |x + --|*|- ---------------- - --------------|
          \    2 / |            2            /    pi\  |
                   |       1 + x          sin|x + --|  |
                   \                         \    2 /  /
(−sin⁡(x)acot⁡(x)sin⁡(x+π2)−log⁡(sin⁡(x+π2))x2+1)sin⁡acot⁡(x)(x+π2)\left(- \frac{\sin{\left(x \right)} \operatorname{acot}{\left(x \right)}}{\sin{\left(x + \frac{\pi}{2} \right)}} - \frac{\log{\left(\sin{\left(x + \frac{\pi}{2} \right)} \right)}}{x^{2} + 1}\right) \sin^{\operatorname{acot}{\left(x \right)}}{\left(x + \frac{\pi}{2} \right)} 
              /                           /    pi\\
              |                acot(x)*cos|x - --||
   acot(x)    |  log(cos(x))              \    2 /|
cos       (x)*|- ----------- - -------------------|
              |          2            cos(x)      |
              \     1 + x                         /
(−cos⁡(x−π2)acot⁡(x)cos⁡(x)−log⁡(cos⁡(x))x2+1)cos⁡acot⁡(x)(x)\left(- \frac{\cos{\left(x - \frac{\pi}{2} \right)} \operatorname{acot}{\left(x \right)}}{\cos{\left(x \right)}} - \frac{\log{\left(\cos{\left(x \right)} \right)}}{x^{2} + 1}\right) \cos^{\operatorname{acot}{\left(x \right)}}{\left(x \right)} 
   acot(x)    /  log(cos(x))   acot(x)*sin(x)\
cos       (x)*|- ----------- - --------------|
              |          2         cos(x)    |
              \     1 + x                    /
(−sin⁡(x)acot⁡(x)cos⁡(x)−log⁡(cos⁡(x))x2+1)cos⁡acot⁡(x)(x)\left(- \frac{\sin{\left(x \right)} \operatorname{acot}{\left(x \right)}}{\cos{\left(x \right)}} - \frac{\log{\left(\cos{\left(x \right)} \right)}}{x^{2} + 1}\right) \cos^{\operatorname{acot}{\left(x \right)}}{\left(x \right)} 
                /     /  1   \                 \
        acot(x) |  log|------|                 |
/  1   \        |     \sec(x)/   acot(x)*sec(x)|
|------|       *|- ----------- - --------------|
\sec(x)/        |          2         /    pi\  |
                |     1 + x       sec|x - --|  |
                \                    \    2 /  /
(−acot⁡(x)sec⁡(x)sec⁡(x−π2)−log⁡(1sec⁡(x))x2+1)(1sec⁡(x))acot⁡(x)\left(- \frac{\operatorname{acot}{\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^{2} + 1}\right) \left(\frac{1}{\sec{\left(x \right)}}\right)^{\operatorname{acot}{\left(x \right)}} 
                /     /  1   \                 \
        acot(x) |  log|------|                 |
/  1   \        |     \sec(x)/   acot(x)*sec(x)|
|------|       *|- ----------- - --------------|
\sec(x)/        |          2         csc(x)    |
                \     1 + x                    /
(−acot⁡(x)sec⁡(x)csc⁡(x)−log⁡(1sec⁡(x))x2+1)(1sec⁡(x))acot⁡(x)\left(- \frac{\operatorname{acot}{\left(x \right)} \sec{\left(x \right)}}{\csc{\left(x \right)}} - \frac{\log{\left(\frac{1}{\sec{\left(x \right)}} \right)}}{x^{2} + 1}\right) \left(\frac{1}{\sec{\left(x \right)}}\right)^{\operatorname{acot}{\left(x \right)}} 
                   /     /   /    pi\\                    \
                   |  log|sin|x + --||        2           |
   acot(x)/    pi\ |     \   \    2 //   2*sin (x)*acot(x)|
sin       |x + --|*|- ---------------- - -----------------|
          \    2 / |            2             sin(2*x)    |
                   \       1 + x                          /
(−2sin⁡2(x)acot⁡(x)sin⁡(2x)−log⁡(sin⁡(x+π2))x2+1)sin⁡acot⁡(x)(x+π2)\left(- \frac{2 \sin^{2}{\left(x \right)} \operatorname{acot}{\left(x \right)}}{\sin{\left(2 x \right)}} - \frac{\log{\left(\sin{\left(x + \frac{\pi}{2} \right)} \right)}}{x^{2} + 1}\right) \sin^{\operatorname{acot}{\left(x \right)}}{\left(x + \frac{\pi}{2} \right)} 
sin(x + pi/2)^acot(x)*(-log(sin(x + pi/2))/(1 + x^2) - 2*sin(x)^2*acot(x)/sin(2*x))
Combinatoria [src] 
    acot(x)    /                                       2               \ 
-cos       (x)*\acot(x)*sin(x) + cos(x)*log(cos(x)) + x *acot(x)*sin(x)/ 
-------------------------------------------------------------------------
                             /     2\                                    
                             \1 + x /*cos(x)
−(x2sin⁡(x)acot⁡(x)+log⁡(cos⁡(x))cos⁡(x)+sin⁡(x)acot⁡(x))cos⁡acot⁡(x)(x)(x2+1)cos⁡(x)- \frac{\left(x^{2} \sin{\left(x \right)} \operatorname{acot}{\left(x \right)} + \log{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)} + \sin{\left(x \right)} \operatorname{acot}{\left(x \right)}\right) \cos^{\operatorname{acot}{\left(x \right)}}{\left(x \right)}}{\left(x^{2} + 1\right) \cos{\left(x \right)}} 
-cos(x)^acot(x)*(acot(x)*sin(x) + cos(x)*log(cos(x)) + x^2*acot(x)*sin(x))/((1 + x^2)*cos(x))
Respuesta numérica [src] 
cos(x)^acot(x)*(-log(cos(x))/(1.0 + x^2) - acot(x)*sin(x)/cos(x))
cos(x)^acot(x)*(-log(cos(x))/(1.0 + x^2) - acot(x)*sin(x)/cos(x))
    © Sr Examen – Калькулятор