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Resolución de integrales/ ch(x)/ 1/ch(x)^3

Integral de 1/ch(x)^3 dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 oo            
  /            
 |             
 |     1       
 |  -------- dx
 |      3      
 |  cosh (x)   
 |             
/              
0
∫0∞1cosh⁡3(x) dx\int\limits_{0}^{\infty} \frac{1}{\cosh^{3}{\left(x \right)}}\, dx 
Integral(1/(cosh(x)^3), (x, 0, oo))
Respuesta (Indefinida) [src] 
  /                            /    /x\\                      /x\                         3/x\                 4/x\     /    /x\\           2/x\     /    /x\\
 |                         atan|tanh|-||                  tanh|-|                     tanh |-|             tanh |-|*atan|tanh|-||     2*tanh |-|*atan|tanh|-||
 |    1                        \    \2//                      \2/                          \2/                  \2/     \    \2//            \2/     \    \2//
 | -------- dx = C + ------------------------- + ------------------------- - ------------------------- + ------------------------- + -------------------------
 |     3                     4/x\         2/x\           4/x\         2/x\           4/x\         2/x\           4/x\         2/x\           4/x\         2/x\
 | cosh (x)          1 + tanh |-| + 2*tanh |-|   1 + tanh |-| + 2*tanh |-|   1 + tanh |-| + 2*tanh |-|   1 + tanh |-| + 2*tanh |-|   1 + tanh |-| + 2*tanh |-|
 |                            \2/          \2/            \2/          \2/            \2/          \2/            \2/          \2/            \2/          \2/
/
∫1cosh⁡3(x) dx=C+tanh⁡4(x2)atan⁡(tanh⁡(x2))tanh⁡4(x2)+2tanh⁡2(x2)+1−tanh⁡3(x2)tanh⁡4(x2)+2tanh⁡2(x2)+1+2tanh⁡2(x2)atan⁡(tanh⁡(x2))tanh⁡4(x2)+2tanh⁡2(x2)+1+tanh⁡(x2)tanh⁡4(x2)+2tanh⁡2(x2)+1+atan⁡(tanh⁡(x2))tanh⁡4(x2)+2tanh⁡2(x2)+1\int \frac{1}{\cosh^{3}{\left(x \right)}}\, dx = C + \frac{\tanh^{4}{\left(\frac{x}{2} \right)} \operatorname{atan}{\left(\tanh{\left(\frac{x}{2} \right)} \right)}}{\tanh^{4}{\left(\frac{x}{2} \right)} + 2 \tanh^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{\tanh^{3}{\left(\frac{x}{2} \right)}}{\tanh^{4}{\left(\frac{x}{2} \right)} + 2 \tanh^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{2 \tanh^{2}{\left(\frac{x}{2} \right)} \operatorname{atan}{\left(\tanh{\left(\frac{x}{2} \right)} \right)}}{\tanh^{4}{\left(\frac{x}{2} \right)} + 2 \tanh^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{\tanh{\left(\frac{x}{2} \right)}}{\tanh^{4}{\left(\frac{x}{2} \right)} + 2 \tanh^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{\operatorname{atan}{\left(\tanh{\left(\frac{x}{2} \right)} \right)}}{\tanh^{4}{\left(\frac{x}{2} \right)} + 2 \tanh^{2}{\left(\frac{x}{2} \right)} + 1}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.9002
Trazar el gráfico f(x)
Respuesta [src] 
pi
--
4
π4\frac{\pi}{4} 
=
= 
pi
--
4
π4\frac{\pi}{4} 
pi/4

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

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