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Resolución de integrales/ sh(x)/ (x)^4/ sh(x)^4

Integral de sh(x)^4 dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 log(2)           
    /             
   |              
   |       4      
   |   sinh (x) dx
   |              
  /               
  0
∫0log⁡(2)sinh⁡4(x) dx\int\limits_{0}^{\log{\left(2 \right)}} \sinh^{4}{\left(x \right)}\, dx 
Integral(sinh(x)^4, (x, 0, log(2)))
Respuesta (Indefinida) [src] 
  /                                                                                                               
 |                         3                      4              4            3                      2        2   
 |     4             3*cosh (x)*sinh(x)   3*x*cosh (x)   3*x*sinh (x)   5*sinh (x)*cosh(x)   3*x*cosh (x)*sinh (x)
 | sinh (x) dx = C - ------------------ + ------------ + ------------ + ------------------ - ---------------------
 |                           8                 8              8                 8                      4          
/
∫sinh⁡4(x) dx=C+3xsinh⁡4(x)8−3xsinh⁡2(x)cosh⁡2(x)4+3xcosh⁡4(x)8+5sinh⁡3(x)cosh⁡(x)8−3sinh⁡(x)cosh⁡3(x)8\int \sinh^{4}{\left(x \right)}\, dx = C + \frac{3 x \sinh^{4}{\left(x \right)}}{8} - \frac{3 x \sinh^{2}{\left(x \right)} \cosh^{2}{\left(x \right)}}{4} + \frac{3 x \cosh^{4}{\left(x \right)}}{8} + \frac{5 \sinh^{3}{\left(x \right)} \cosh{\left(x \right)}}{8} - \frac{3 \sinh{\left(x \right)} \cosh^{3}{\left(x \right)}}{8}
Simplificar
Gráfica
0.000.050.100.150.200.250.300.350.400.450.500.550.600.650.00.5
Trazar el gráfico f(x)
Respuesta [src] 
        3                              4                        4                        3                              2             2               
  3*cosh (log(2))*sinh(log(2))   3*cosh (log(2))*log(2)   3*sinh (log(2))*log(2)   5*sinh (log(2))*cosh(log(2))   3*cosh (log(2))*sinh (log(2))*log(2)
- ---------------------------- + ---------------------- + ---------------------- + ---------------------------- - ------------------------------------
               8                           8                        8                           8                                  4
−3sinh⁡(log⁡(2))cosh⁡3(log⁡(2))8−3log⁡(2)sinh⁡2(log⁡(2))cosh⁡2(log⁡(2))4+3log⁡(2)sinh⁡4(log⁡(2))8+5sinh⁡3(log⁡(2))cosh⁡(log⁡(2))8+3log⁡(2)cosh⁡4(log⁡(2))8- \frac{3 \sinh{\left(\log{\left(2 \right)} \right)} \cosh^{3}{\left(\log{\left(2 \right)} \right)}}{8} - \frac{3 \log{\left(2 \right)} \sinh^{2}{\left(\log{\left(2 \right)} \right)} \cosh^{2}{\left(\log{\left(2 \right)} \right)}}{4} + \frac{3 \log{\left(2 \right)} \sinh^{4}{\left(\log{\left(2 \right)} \right)}}{8} + \frac{5 \sinh^{3}{\left(\log{\left(2 \right)} \right)} \cosh{\left(\log{\left(2 \right)} \right)}}{8} + \frac{3 \log{\left(2 \right)} \cosh^{4}{\left(\log{\left(2 \right)} \right)}}{8} 
=
= 
        3                              4                        4                        3                              2             2               
  3*cosh (log(2))*sinh(log(2))   3*cosh (log(2))*log(2)   3*sinh (log(2))*log(2)   5*sinh (log(2))*cosh(log(2))   3*cosh (log(2))*sinh (log(2))*log(2)
- ---------------------------- + ---------------------- + ---------------------- + ---------------------------- - ------------------------------------
               8                           8                        8                           8                                  4
−3sinh⁡(log⁡(2))cosh⁡3(log⁡(2))8−3log⁡(2)sinh⁡2(log⁡(2))cosh⁡2(log⁡(2))4+3log⁡(2)sinh⁡4(log⁡(2))8+5sinh⁡3(log⁡(2))cosh⁡(log⁡(2))8+3log⁡(2)cosh⁡4(log⁡(2))8- \frac{3 \sinh{\left(\log{\left(2 \right)} \right)} \cosh^{3}{\left(\log{\left(2 \right)} \right)}}{8} - \frac{3 \log{\left(2 \right)} \sinh^{2}{\left(\log{\left(2 \right)} \right)} \cosh^{2}{\left(\log{\left(2 \right)} \right)}}{4} + \frac{3 \log{\left(2 \right)} \sinh^{4}{\left(\log{\left(2 \right)} \right)}}{8} + \frac{5 \sinh^{3}{\left(\log{\left(2 \right)} \right)} \cosh{\left(\log{\left(2 \right)} \right)}}{8} + \frac{3 \log{\left(2 \right)} \cosh^{4}{\left(\log{\left(2 \right)} \right)}}{8} 
-3*cosh(log(2))^3*sinh(log(2))/8 + 3*cosh(log(2))^4*log(2)/8 + 3*sinh(log(2))^4*log(2)/8 + 5*sinh(log(2))^3*cosh(log(2))/8 - 3*cosh(log(2))^2*sinh(log(2))^2*log(2)/4
Respuesta numérica [src] 
0.0402036302099795
0.0402036302099795

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

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