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Integral de d{x}:
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Expresiones idénticas
- uno /(2siny*cosy^ tres)
menos 1 dividir por (2 seno de y multiplicar por coseno de y al cubo )
menos uno dividir por (2 seno de y multiplicar por coseno de y en el grado tres)
-1/(2siny*cosy3)
-1/2siny*cosy3
-1/(2siny*cosy³)
-1/(2siny*cosy en el grado 3)
-1/(2sinycosy^3)
-1/(2sinycosy3)
-1/2sinycosy3
-1/2sinycosy^3
-1 dividir por (2siny*cosy^3)
Expresiones semejantes
1/(2siny*cosy^3)

Resolución de integrales/ -1/(2siny*cosy^3)

Integral de -1/(2siny*cosy^3) dy

Solución

Ha introducido [src]

  1                    
  /                    
 |                     
 |        -1           
 |  ---------------- dy
 |              3      
 |  2*sin(y)*cos (y)   
 |                     
/                      
0

$$\int\limits_{0}^{1} \left(- \frac{1}{2 \sin{\left(y \right)} \cos^{3}{\left(y \right)}}\right)\, dy$$

Integral(-1/((2*sin(y))*cos(y)^3), (y, 0, 1))

Solución detallada

La integral del producto de una función por una constante es la constante por la integral de esta función:

$\int \left(- \frac{1}{2 \sin{\left(y \right)} \cos^{3}{\left(y \right)}}\right)\, dy = - \int \frac{1}{2 \sin{\left(y \right)} \cos^{3}{\left(y \right)}}\, dy$
1. No puedo encontrar los pasos en la búsqueda de esta integral.
  
  Pero la integral
  
  $- \frac{\log{\left(\tan{\left(\frac{y}{2} \right)} - 1 \right)} \tan^{4}{\left(\frac{y}{2} \right)}}{2 \tan^{4}{\left(\frac{y}{2} \right)} - 4 \tan^{2}{\left(\frac{y}{2} \right)} + 2} + \frac{2 \log{\left(\tan{\left(\frac{y}{2} \right)} - 1 \right)} \tan^{2}{\left(\frac{y}{2} \right)}}{2 \tan^{4}{\left(\frac{y}{2} \right)} - 4 \tan^{2}{\left(\frac{y}{2} \right)} + 2} - \frac{\log{\left(\tan{\left(\frac{y}{2} \right)} - 1 \right)}}{2 \tan^{4}{\left(\frac{y}{2} \right)} - 4 \tan^{2}{\left(\frac{y}{2} \right)} + 2} - \frac{\log{\left(\tan{\left(\frac{y}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{y}{2} \right)}}{2 \tan^{4}{\left(\frac{y}{2} \right)} - 4 \tan^{2}{\left(\frac{y}{2} \right)} + 2} + \frac{2 \log{\left(\tan{\left(\frac{y}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{y}{2} \right)}}{2 \tan^{4}{\left(\frac{y}{2} \right)} - 4 \tan^{2}{\left(\frac{y}{2} \right)} + 2} - \frac{\log{\left(\tan{\left(\frac{y}{2} \right)} + 1 \right)}}{2 \tan^{4}{\left(\frac{y}{2} \right)} - 4 \tan^{2}{\left(\frac{y}{2} \right)} + 2} + \frac{\log{\left(\tan{\left(\frac{y}{2} \right)} \right)} \tan^{4}{\left(\frac{y}{2} \right)}}{2 \tan^{4}{\left(\frac{y}{2} \right)} - 4 \tan^{2}{\left(\frac{y}{2} \right)} + 2} - \frac{2 \log{\left(\tan{\left(\frac{y}{2} \right)} \right)} \tan^{2}{\left(\frac{y}{2} \right)}}{2 \tan^{4}{\left(\frac{y}{2} \right)} - 4 \tan^{2}{\left(\frac{y}{2} \right)} + 2} + \frac{\log{\left(\tan{\left(\frac{y}{2} \right)} \right)}}{2 \tan^{4}{\left(\frac{y}{2} \right)} - 4 \tan^{2}{\left(\frac{y}{2} \right)} + 2} + \frac{2 \tan^{2}{\left(\frac{y}{2} \right)}}{2 \tan^{4}{\left(\frac{y}{2} \right)} - 4 \tan^{2}{\left(\frac{y}{2} \right)} + 2}$
Por lo tanto, el resultado es: $\frac{\log{\left(\tan{\left(\frac{y}{2} \right)} - 1 \right)} \tan^{4}{\left(\frac{y}{2} \right)}}{2 \tan^{4}{\left(\frac{y}{2} \right)} - 4 \tan^{2}{\left(\frac{y}{2} \right)} + 2} - \frac{2 \log{\left(\tan{\left(\frac{y}{2} \right)} - 1 \right)} \tan^{2}{\left(\frac{y}{2} \right)}}{2 \tan^{4}{\left(\frac{y}{2} \right)} - 4 \tan^{2}{\left(\frac{y}{2} \right)} + 2} + \frac{\log{\left(\tan{\left(\frac{y}{2} \right)} - 1 \right)}}{2 \tan^{4}{\left(\frac{y}{2} \right)} - 4 \tan^{2}{\left(\frac{y}{2} \right)} + 2} + \frac{\log{\left(\tan{\left(\frac{y}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{y}{2} \right)}}{2 \tan^{4}{\left(\frac{y}{2} \right)} - 4 \tan^{2}{\left(\frac{y}{2} \right)} + 2} - \frac{2 \log{\left(\tan{\left(\frac{y}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{y}{2} \right)}}{2 \tan^{4}{\left(\frac{y}{2} \right)} - 4 \tan^{2}{\left(\frac{y}{2} \right)} + 2} + \frac{\log{\left(\tan{\left(\frac{y}{2} \right)} + 1 \right)}}{2 \tan^{4}{\left(\frac{y}{2} \right)} - 4 \tan^{2}{\left(\frac{y}{2} \right)} + 2} - \frac{\log{\left(\tan{\left(\frac{y}{2} \right)} \right)} \tan^{4}{\left(\frac{y}{2} \right)}}{2 \tan^{4}{\left(\frac{y}{2} \right)} - 4 \tan^{2}{\left(\frac{y}{2} \right)} + 2} + \frac{2 \log{\left(\tan{\left(\frac{y}{2} \right)} \right)} \tan^{2}{\left(\frac{y}{2} \right)}}{2 \tan^{4}{\left(\frac{y}{2} \right)} - 4 \tan^{2}{\left(\frac{y}{2} \right)} + 2} - \frac{\log{\left(\tan{\left(\frac{y}{2} \right)} \right)}}{2 \tan^{4}{\left(\frac{y}{2} \right)} - 4 \tan^{2}{\left(\frac{y}{2} \right)} + 2} - \frac{2 \tan^{2}{\left(\frac{y}{2} \right)}}{2 \tan^{4}{\left(\frac{y}{2} \right)} - 4 \tan^{2}{\left(\frac{y}{2} \right)} + 2}$
Ahora simplificar:

$\frac{\left(\tan{\left(\frac{y}{2} \right)} - 1\right)^{2} \left(\tan{\left(\frac{y}{2} \right)} + 1\right)^{2} \left(\left(\cos{\left(y \right)} - 1\right)^{2} \log{\left(\tan{\left(\frac{y}{2} \right)} - 1 \right)} + \left(\cos{\left(y \right)} - 1\right)^{2} \log{\left(\tan{\left(\frac{y}{2} \right)} + 1 \right)} - \left(\cos{\left(y \right)} - 1\right)^{2} \log{\left(\tan{\left(\frac{y}{2} \right)} \right)} + \left(\cos{\left(2 y \right)} - 1\right) \log{\left(\tan{\left(\frac{y}{2} \right)} - 1 \right)} + \left(\cos{\left(2 y \right)} - 1\right) \log{\left(\tan{\left(\frac{y}{2} \right)} + 1 \right)} - \left(\cos{\left(2 y \right)} - 1\right) \log{\left(\tan{\left(\frac{y}{2} \right)} \right)} + \cos{\left(2 y \right)} - 1\right) + 4 \left(\log{\left(\tan{\left(\frac{y}{2} \right)} - 1 \right)} + \log{\left(\tan{\left(\frac{y}{2} \right)} + 1 \right)} - \log{\left(\tan{\left(\frac{y}{2} \right)} \right)}\right) \cos^{2}{\left(y \right)}}{8 \left(\tan{\left(\frac{y}{2} \right)} - 1\right)^{2} \left(\tan{\left(\frac{y}{2} \right)} + 1\right)^{2} \cos^{2}{\left(y \right)}}$
Añadimos la constante de integración:

$\frac{\left(\tan{\left(\frac{y}{2} \right)} - 1\right)^{2} \left(\tan{\left(\frac{y}{2} \right)} + 1\right)^{2} \left(\left(\cos{\left(y \right)} - 1\right)^{2} \log{\left(\tan{\left(\frac{y}{2} \right)} - 1 \right)} + \left(\cos{\left(y \right)} - 1\right)^{2} \log{\left(\tan{\left(\frac{y}{2} \right)} + 1 \right)} - \left(\cos{\left(y \right)} - 1\right)^{2} \log{\left(\tan{\left(\frac{y}{2} \right)} \right)} + \left(\cos{\left(2 y \right)} - 1\right) \log{\left(\tan{\left(\frac{y}{2} \right)} - 1 \right)} + \left(\cos{\left(2 y \right)} - 1\right) \log{\left(\tan{\left(\frac{y}{2} \right)} + 1 \right)} - \left(\cos{\left(2 y \right)} - 1\right) \log{\left(\tan{\left(\frac{y}{2} \right)} \right)} + \cos{\left(2 y \right)} - 1\right) + 4 \left(\log{\left(\tan{\left(\frac{y}{2} \right)} - 1 \right)} + \log{\left(\tan{\left(\frac{y}{2} \right)} + 1 \right)} - \log{\left(\tan{\left(\frac{y}{2} \right)} \right)}\right) \cos^{2}{\left(y \right)}}{8 \left(\tan{\left(\frac{y}{2} \right)} - 1\right)^{2} \left(\tan{\left(\frac{y}{2} \right)} + 1\right)^{2} \cos^{2}{\left(y \right)}}+ \mathrm{constant}$

Respuesta:

$\frac{\left(\tan{\left(\frac{y}{2} \right)} - 1\right)^{2} \left(\tan{\left(\frac{y}{2} \right)} + 1\right)^{2} \left(\left(\cos{\left(y \right)} - 1\right)^{2} \log{\left(\tan{\left(\frac{y}{2} \right)} - 1 \right)} + \left(\cos{\left(y \right)} - 1\right)^{2} \log{\left(\tan{\left(\frac{y}{2} \right)} + 1 \right)} - \left(\cos{\left(y \right)} - 1\right)^{2} \log{\left(\tan{\left(\frac{y}{2} \right)} \right)} + \left(\cos{\left(2 y \right)} - 1\right) \log{\left(\tan{\left(\frac{y}{2} \right)} - 1 \right)} + \left(\cos{\left(2 y \right)} - 1\right) \log{\left(\tan{\left(\frac{y}{2} \right)} + 1 \right)} - \left(\cos{\left(2 y \right)} - 1\right) \log{\left(\tan{\left(\frac{y}{2} \right)} \right)} + \cos{\left(2 y \right)} - 1\right) + 4 \left(\log{\left(\tan{\left(\frac{y}{2} \right)} - 1 \right)} + \log{\left(\tan{\left(\frac{y}{2} \right)} + 1 \right)} - \log{\left(\tan{\left(\frac{y}{2} \right)} \right)}\right) \cos^{2}{\left(y \right)}}{8 \left(\tan{\left(\frac{y}{2} \right)} - 1\right)^{2} \left(\tan{\left(\frac{y}{2} \right)} + 1\right)^{2} \cos^{2}{\left(y \right)}}+ \mathrm{constant}$

Respuesta (Indefinida) [src]

  /                                  /       /y\\                /        /y\\                 /   /y\\                       2/y\               4/y\    /       /y\\        4/y\    /        /y\\         4/y\    /   /y\\           2/y\    /       /y\\        2/y\    /        /y\\          2/y\    /   /y\\  
 |                                log|1 + tan|-||             log|-1 + tan|-||              log|tan|-||                  2*tan |-|            tan |-|*log|1 + tan|-||     tan |-|*log|-1 + tan|-||      tan |-|*log|tan|-||      2*tan |-|*log|1 + tan|-||   2*tan |-|*log|-1 + tan|-||     2*tan |-|*log|tan|-||  
 |       -1                          \       \2//                \        \2//                 \   \2//                        \2/                \2/    \       \2//         \2/    \        \2//          \2/    \   \2//            \2/    \       \2//         \2/    \        \2//           \2/    \   \2//  
 | ---------------- dy = C + ------------------------- + ------------------------- - ------------------------- - ------------------------- + ------------------------- + ------------------------- - ------------------------- - ------------------------- - -------------------------- + -------------------------
 |             3                      2/y\        4/y\            2/y\        4/y\            2/y\        4/y\            2/y\        4/y\            2/y\        4/y\            2/y\        4/y\            2/y\        4/y\            2/y\        4/y\            2/y\        4/y\             2/y\        4/y\
 | 2*sin(y)*cos (y)          2 - 4*tan |-| + 2*tan |-|   2 - 4*tan |-| + 2*tan |-|   2 - 4*tan |-| + 2*tan |-|   2 - 4*tan |-| + 2*tan |-|   2 - 4*tan |-| + 2*tan |-|   2 - 4*tan |-| + 2*tan |-|   2 - 4*tan |-| + 2*tan |-|   2 - 4*tan |-| + 2*tan |-|   2 - 4*tan |-| + 2*tan |-|    2 - 4*tan |-| + 2*tan |-|
 |                                     \2/         \2/             \2/         \2/             \2/         \2/             \2/         \2/             \2/         \2/             \2/         \2/             \2/         \2/             \2/         \2/             \2/         \2/              \2/         \2/
/

$$\int \left(- \frac{1}{2 \sin{\left(y \right)} \cos^{3}{\left(y \right)}}\right)\, dy = C + \frac{\log{\left(\tan{\left(\frac{y}{2} \right)} - 1 \right)} \tan^{4}{\left(\frac{y}{2} \right)}}{2 \tan^{4}{\left(\frac{y}{2} \right)} - 4 \tan^{2}{\left(\frac{y}{2} \right)} + 2} - \frac{2 \log{\left(\tan{\left(\frac{y}{2} \right)} - 1 \right)} \tan^{2}{\left(\frac{y}{2} \right)}}{2 \tan^{4}{\left(\frac{y}{2} \right)} - 4 \tan^{2}{\left(\frac{y}{2} \right)} + 2} + \frac{\log{\left(\tan{\left(\frac{y}{2} \right)} - 1 \right)}}{2 \tan^{4}{\left(\frac{y}{2} \right)} - 4 \tan^{2}{\left(\frac{y}{2} \right)} + 2} + \frac{\log{\left(\tan{\left(\frac{y}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{y}{2} \right)}}{2 \tan^{4}{\left(\frac{y}{2} \right)} - 4 \tan^{2}{\left(\frac{y}{2} \right)} + 2} - \frac{2 \log{\left(\tan{\left(\frac{y}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{y}{2} \right)}}{2 \tan^{4}{\left(\frac{y}{2} \right)} - 4 \tan^{2}{\left(\frac{y}{2} \right)} + 2} + \frac{\log{\left(\tan{\left(\frac{y}{2} \right)} + 1 \right)}}{2 \tan^{4}{\left(\frac{y}{2} \right)} - 4 \tan^{2}{\left(\frac{y}{2} \right)} + 2} - \frac{\log{\left(\tan{\left(\frac{y}{2} \right)} \right)} \tan^{4}{\left(\frac{y}{2} \right)}}{2 \tan^{4}{\left(\frac{y}{2} \right)} - 4 \tan^{2}{\left(\frac{y}{2} \right)} + 2} + \frac{2 \log{\left(\tan{\left(\frac{y}{2} \right)} \right)} \tan^{2}{\left(\frac{y}{2} \right)}}{2 \tan^{4}{\left(\frac{y}{2} \right)} - 4 \tan^{2}{\left(\frac{y}{2} \right)} + 2} - \frac{\log{\left(\tan{\left(\frac{y}{2} \right)} \right)}}{2 \tan^{4}{\left(\frac{y}{2} \right)} - 4 \tan^{2}{\left(\frac{y}{2} \right)} + 2} - \frac{2 \tan^{2}{\left(\frac{y}{2} \right)}}{2 \tan^{4}{\left(\frac{y}{2} \right)} - 4 \tan^{2}{\left(\frac{y}{2} \right)} + 2}$$

Simplificar

Gráfica

Trazar el gráfico f(x)

Respuesta [src]

      pi*I
-oo - ----
       4

$$-\infty - \frac{i \pi}{4}$$

      pi*I
-oo - ----
       4

$$-\infty - \frac{i \pi}{4}$$

-oo - pi*i/4

Respuesta numérica [src]

-22.8731141342586

-22.8731141342586

Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

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Expresiones idénticas

Expresiones semejantes

Integral de -1/(2siny*cosy^3) dy

Límites de integración:

Gráfico:

Definida a trozos:

Solución