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Resolución de integrales/ (x)^2/ ch(x)/ sh(x)/ sh(x)^2ch(x)^2

Integral de sh(x)^2ch(x)^2 dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                     
  /                     
 |                      
 |      2        2      
 |  sinh (x)*cosh (x) dx
 |                      
/                       
0
∫01sinh⁡2(x)cosh⁡2(x) dx\int\limits_{0}^{1} \sinh^{2}{\left(x \right)} \cosh^{2}{\left(x \right)}\, dx 
Integral(sinh(x)^2*cosh(x)^2, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                                              
 |                                  4            4          3                  3                    2        2   
 |     2        2             x*cosh (x)   x*sinh (x)   cosh (x)*sinh(x)   sinh (x)*cosh(x)   x*cosh (x)*sinh (x)
 | sinh (x)*cosh (x) dx = C - ---------- - ---------- + ---------------- + ---------------- + -------------------
 |                                8            8               8                  8                    4         
/
∫sinh⁡2(x)cosh⁡2(x) dx=C−xsinh⁡4(x)8+xsinh⁡2(x)cosh⁡2(x)4−xcosh⁡4(x)8+sinh⁡3(x)cosh⁡(x)8+sinh⁡(x)cosh⁡3(x)8\int \sinh^{2}{\left(x \right)} \cosh^{2}{\left(x \right)}\, dx = C - \frac{x \sinh^{4}{\left(x \right)}}{8} + \frac{x \sinh^{2}{\left(x \right)} \cosh^{2}{\left(x \right)}}{4} - \frac{x \cosh^{4}{\left(x \right)}}{8} + \frac{\sinh^{3}{\left(x \right)} \cosh{\left(x \right)}}{8} + \frac{\sinh{\left(x \right)} \cosh^{3}{\left(x \right)}}{8}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.9005
Trazar el gráfico f(x)
Respuesta [src] 
      4          4          2        2          3                  3           
  cosh (1)   sinh (1)   cosh (1)*sinh (1)   cosh (1)*sinh(1)   sinh (1)*cosh(1)
- -------- - -------- + ----------------- + ---------------- + ----------------
     8          8               4                  8                  8
−cosh⁡4(1)8−sinh⁡4(1)8+sinh⁡3(1)cosh⁡(1)8+sinh⁡(1)cosh⁡3(1)8+sinh⁡2(1)cosh⁡2(1)4- \frac{\cosh^{4}{\left(1 \right)}}{8} - \frac{\sinh^{4}{\left(1 \right)}}{8} + \frac{\sinh^{3}{\left(1 \right)} \cosh{\left(1 \right)}}{8} + \frac{\sinh{\left(1 \right)} \cosh^{3}{\left(1 \right)}}{8} + \frac{\sinh^{2}{\left(1 \right)} \cosh^{2}{\left(1 \right)}}{4} 
=
= 
      4          4          2        2          3                  3           
  cosh (1)   sinh (1)   cosh (1)*sinh (1)   cosh (1)*sinh(1)   sinh (1)*cosh(1)
- -------- - -------- + ----------------- + ---------------- + ----------------
     8          8               4                  8                  8
−cosh⁡4(1)8−sinh⁡4(1)8+sinh⁡3(1)cosh⁡(1)8+sinh⁡(1)cosh⁡3(1)8+sinh⁡2(1)cosh⁡2(1)4- \frac{\cosh^{4}{\left(1 \right)}}{8} - \frac{\sinh^{4}{\left(1 \right)}}{8} + \frac{\sinh^{3}{\left(1 \right)} \cosh{\left(1 \right)}}{8} + \frac{\sinh{\left(1 \right)} \cosh^{3}{\left(1 \right)}}{8} + \frac{\sinh^{2}{\left(1 \right)} \cosh^{2}{\left(1 \right)}}{4} 
-cosh(1)^4/8 - sinh(1)^4/8 + cosh(1)^2*sinh(1)^2/4 + cosh(1)^3*sinh(1)/8 + sinh(1)^3*cosh(1)/8
Respuesta numérica [src] 
0.727809912410242
0.727809912410242

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

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