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

Integral de 1/(sh(x)*ch^3(x)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                    
  /                    
 |                     
 |         1           
 |  ---------------- dx
 |              3      
 |  sinh(x)*cosh (x)   
 |                     
/                      
0
∫011sinh⁡(x)cosh⁡3(x) dx\int\limits_{0}^{1} \frac{1}{\sinh{\left(x \right)} \cosh^{3}{\left(x \right)}}\, dx 
Integral(1/(sinh(x)*cosh(x)^3), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                    /    /x\\                /        2/x\\                     2/x\                4/x\    /    /x\\         4/x\    /        2/x\\         2/x\    /        2/x\\          2/x\    /    /x\\ 
 |                                  log|tanh|-||             log|1 + tanh |-||               2*tanh |-|            tanh |-|*log|tanh|-||     tanh |-|*log|1 + tanh |-||   2*tanh |-|*log|1 + tanh |-||    2*tanh |-|*log|tanh|-|| 
 |        1                            \    \2//                \         \2//                      \2/                 \2/    \    \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\             4/x\         2/x\             4/x\         2/x\
 | sinh(x)*cosh (x)          1 + tanh |-| + 2*tanh |-|   1 + tanh |-| + 2*tanh |-|   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/              \2/          \2/              \2/          \2/
/
∫1sinh⁡(x)cosh⁡3(x) dx=C−log⁡(tanh⁡2(x2)+1)tanh⁡4(x2)tanh⁡4(x2)+2tanh⁡2(x2)+1−2log⁡(tanh⁡2(x2)+1)tanh⁡2(x2)tanh⁡4(x2)+2tanh⁡2(x2)+1−log⁡(tanh⁡2(x2)+1)tanh⁡4(x2)+2tanh⁡2(x2)+1+log⁡(tanh⁡(x2))tanh⁡4(x2)tanh⁡4(x2)+2tanh⁡2(x2)+1+2log⁡(tanh⁡(x2))tanh⁡2(x2)tanh⁡4(x2)+2tanh⁡2(x2)+1+log⁡(tanh⁡(x2))tanh⁡4(x2)+2tanh⁡2(x2)+1−2tanh⁡2(x2)tanh⁡4(x2)+2tanh⁡2(x2)+1\int \frac{1}{\sinh{\left(x \right)} \cosh^{3}{\left(x \right)}}\, dx = C - \frac{\log{\left(\tanh^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tanh^{4}{\left(\frac{x}{2} \right)}}{\tanh^{4}{\left(\frac{x}{2} \right)} + 2 \tanh^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{2 \log{\left(\tanh^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tanh^{2}{\left(\frac{x}{2} \right)}}{\tanh^{4}{\left(\frac{x}{2} \right)} + 2 \tanh^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{\log{\left(\tanh^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{\tanh^{4}{\left(\frac{x}{2} \right)} + 2 \tanh^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{\log{\left(\tanh{\left(\frac{x}{2} \right)} \right)} \tanh^{4}{\left(\frac{x}{2} \right)}}{\tanh^{4}{\left(\frac{x}{2} \right)} + 2 \tanh^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{2 \log{\left(\tanh{\left(\frac{x}{2} \right)} \right)} \tanh^{2}{\left(\frac{x}{2} \right)}}{\tanh^{4}{\left(\frac{x}{2} \right)} + 2 \tanh^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{\log{\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{2 \tanh^{2}{\left(\frac{x}{2} \right)}}{\tanh^{4}{\left(\frac{x}{2} \right)} + 2 \tanh^{2}{\left(\frac{x}{2} \right)} + 1}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.90-500010000
Trazar el gráfico f(x)
Respuesta [src] 
oo
∞\infty 
=
= 
oo
∞\infty 
oo
Respuesta numérica [src] 
43.5280918358881
43.5280918358881

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

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