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Resolución de integrales/ sinh^4(x)

Integral de sinh^4(x) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1            
  /            
 |             
 |      4      
 |  sinh (x) dx
 |             
/              
0
$$\int\limits_{0}^{1} \sinh^{4}{\left(x \right)}\, dx$$ 
Integral(sinh(x)^4, (x, 0, 1))
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          
/
$$\int \sinh^{4}{\left(x \right)}\, dx = C + \frac{3 x \sinh^{4}{\left(x \right)}}{8} - \frac{3 x \sinh^{2}{\left(x \right)} \cosh^{2}{\left(x \right)}}{4} + \frac{3 x \cosh^{4}{\left(x \right)}}{8} + \frac{5 \sinh^{3}{\left(x \right)} \cosh{\left(x \right)}}{8} - \frac{3 \sinh{\left(x \right)} \cosh^{3}{\left(x \right)}}{8}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
      4            4            2        2            3                    3           
3*cosh (1)   3*sinh (1)   3*cosh (1)*sinh (1)   3*cosh (1)*sinh(1)   5*sinh (1)*cosh(1)
---------- + ---------- - ------------------- - ------------------ + ------------------
    8            8                 4                    8                    8
$$- \frac{3 \sinh^{2}{\left(1 \right)} \cosh^{2}{\left(1 \right)}}{4} - \frac{3 \sinh{\left(1 \right)} \cosh^{3}{\left(1 \right)}}{8} + \frac{3 \sinh^{4}{\left(1 \right)}}{8} + \frac{5 \sinh^{3}{\left(1 \right)} \cosh{\left(1 \right)}}{8} + \frac{3 \cosh^{4}{\left(1 \right)}}{8}$$ 
=
= 
      4            4            2        2            3                    3           
3*cosh (1)   3*sinh (1)   3*cosh (1)*sinh (1)   3*cosh (1)*sinh(1)   5*sinh (1)*cosh(1)
---------- + ---------- - ------------------- - ------------------ + ------------------
    8            8                 4                    8                    8
$$- \frac{3 \sinh^{2}{\left(1 \right)} \cosh^{2}{\left(1 \right)}}{4} - \frac{3 \sinh{\left(1 \right)} \cosh^{3}{\left(1 \right)}}{8} + \frac{3 \sinh^{4}{\left(1 \right)}}{8} + \frac{5 \sinh^{3}{\left(1 \right)} \cosh{\left(1 \right)}}{8} + \frac{3 \cosh^{4}{\left(1 \right)}}{8}$$ 
3*cosh(1)^4/8 + 3*sinh(1)^4/8 - 3*cosh(1)^2*sinh(1)^2/4 - 3*cosh(1)^3*sinh(1)/8 + 5*sinh(1)^3*cosh(1)/8
Respuesta numérica [src] 
0.321094810448488
0.321094810448488

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

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