Integral of chxshx dx

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

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

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

Detail solution

There are multiple ways to do this integral.
Method #1
1. Let $u = \cosh{\left(x \right)}$ .
  
  Then let $du = \sinh{\left(x \right)} dx$ and substitute $du$ :
  
  $\int u\, du$
  1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int u\, du = \frac{u^{2}}{2}$
  Now substitute $u$ back in:
  
  $\frac{\cosh^{2}{\left(x \right)}}{2}$
Method #2
1. Let $u = \sinh{\left(x \right)}$ .
  
  Then let $du = \cosh{\left(x \right)} dx$ and substitute $du$ :
  
  $\int u\, du$
  1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int u\, du = \frac{u^{2}}{2}$
  Now substitute $u$ back in:
  
  $\frac{\sinh^{2}{\left(x \right)}}{2}$
Add the constant of integration:

$\frac{\cosh^{2}{\left(x \right)}}{2}+ \mathrm{constant}$

The answer is:

$\frac{\cosh^{2}{\left(x \right)}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                             2   
 |                          cosh (x)
 | cosh(x)*sinh(x) dx = C + --------
 |                             2    
/

$$\int \sinh{\left(x \right)} \cosh{\left(x \right)}\, dx = C + \frac{\cosh^{2}{\left(x \right)}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

          2   
  1   cosh (1)
- - + --------
  2      2

$$- \frac{1}{2} + \frac{\cosh^{2}{\left(1 \right)}}{2}$$

          2   
  1   cosh (1)
- - + --------
  2      2

$$- \frac{1}{2} + \frac{\cosh^{2}{\left(1 \right)}}{2}$$

-1/2 + cosh(1)^2/2

Numerical answer [src]

0.690548922770908

0.690548922770908

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

Method #1