Mister Exam

Integral of ch(x)sh(x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  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
  1. There are multiple ways to do this integral.

    Method #1

    1. Let .

      Then let and substitute :

      1. The integral of is when :

      Now substitute back in:

    Method #2

    1. Let .

      Then let and substitute :

      1. The integral of is when :

      Now substitute back in:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                             2   
 |                          cosh (x)
 | cosh(x)*sinh(x) dx = C + --------
 |                             2    
/                                   
$${{\cosh ^2x}\over{2}}$$
The graph
The answer [src]
          2   
  1   cosh (1)
- - + --------
  2      2    
$${{\cosh ^21}\over{2}}-{{1}\over{2}}$$
=
=
          2   
  1   cosh (1)
- - + --------
  2      2    
$$- \frac{1}{2} + \frac{\cosh^{2}{\left(1 \right)}}{2}$$
Numerical answer [src]
0.690548922770908
0.690548922770908
The graph
Integral of ch(x)sh(x) dx

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