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Identical expressions
sinh^3xcoshx
hyperbolic sinus of e of cubed x hyperbolic co sinus of e of ine of x
sinh3xcoshx
sinh³xcoshx
sinh to the power of 3xcoshx
sinh^3xcoshxdx

Integral of sinh^3xcoshx dx

The solution

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  1                    
  /                    
 |                     
 |      3              
 |  sinh (x)*cosh(x) dx
 |                     
/                      
0

$$\int\limits_{0}^{1} \sinh^{3}{\left(x \right)} \cosh{\left(x \right)}\, dx$$

Integral(sinh(x)^3*cosh(x), (x, 0, 1))

Detail solution

Let $u = \sinh{\left(x \right)}$ .

Then let $du = \cosh{\left(x \right)} dx$ and substitute $du$ :

$\int u^{3}\, du$
1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int u^{3}\, du = \frac{u^{4}}{4}$
Now substitute $u$ back in:

$\frac{\sinh^{4}{\left(x \right)}}{4}$
Add the constant of integration:

$\frac{\sinh^{4}{\left(x \right)}}{4}+ \mathrm{constant}$

The answer is:

$\frac{\sinh^{4}{\left(x \right)}}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                  
 |                               4   
 |     3                     sinh (x)
 | sinh (x)*cosh(x) dx = C + --------
 |                              4    
/

$$\int \sinh^{3}{\left(x \right)} \cosh{\left(x \right)}\, dx = C + \frac{\sinh^{4}{\left(x \right)}}{4}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

    4   
sinh (1)
--------
   4

$$\frac{\sinh^{4}{\left(1 \right)}}{4}$$

    4   
sinh (1)
--------
   4

$$\frac{\sinh^{4}{\left(1 \right)}}{4}$$

sinh(1)^4/4

Numerical answer [src]

0.476857814740061

0.476857814740061

Use the examples entering the upper and lower limits of integration.

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Identical expressions

Integral of sinh^3xcoshx dx

Limits of integration:

The graph:

Piecewise:

The solution