Integral of sh(2x) dx

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  1             
  /             
 |              
 |  sinh(2*x) dx
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0

$$\int\limits_{0}^{1} \sinh{\left(2 x \right)}\, dx$$

Simplify

Detail solution

Let $u = 2 x$ .

Then let $du = 2 dx$ and substitute $\frac{du}{2}$ :

$\int \frac{\sinh{\left(u \right)}}{4}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{\sinh{\left(u \right)}}{2}\, du = \frac{\int \sinh{\left(u \right)}\, du}{2}$
  So, the result is: $\frac{\cosh{\left(u \right)}}{2}$
Now substitute $u$ back in:

$\frac{\cosh{\left(2 x \right)}}{2}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

$${{\cosh \left(2\,x\right)}\over{2}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

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

$${{\cosh 2}\over{2}}-{{1}\over{2}}$$

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

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

Simplify

Numerical answer [src]

1.38109784554182

1.38109784554182

The graph

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