Integral of sinh(3x) dx

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

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

Detail solution

Let $u = 3 x$ .

Then let $du = 3 dx$ and substitute $\frac{du}{3}$ :

$\int \frac{\sinh{\left(u \right)}}{9}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{\sinh{\left(u \right)}}{3}\, du = \frac{\int \sinh{\left(u \right)}\, du}{3}$
  So, the result is: $\frac{\cosh{\left(u \right)}}{3}$
Now substitute $u$ back in:

$\frac{\cosh{\left(3 x \right)}}{3}$
Add the constant of integration:

$\frac{\cosh{\left(3 x \right)}}{3}+ \mathrm{constant}$

The answer is:

$\frac{\cosh{\left(3 x \right)}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                            
 |                    cosh(3*x)
 | sinh(3*x) dx = C + ---------
 |                        3    
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$${{\cosh \left(3\,x\right)}\over{3}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

  1   cosh(3)
- - + -------
  3      3

$${{\cosh 3}\over{3}}-{{1}\over{3}}$$

  1   cosh(3)
- - + -------
  3      3

$$- \frac{1}{3} + \frac{\cosh{\left(3 \right)}}{3}$$

Simplify

Numerical answer [src]

3.02255399859259

3.02255399859259

The graph

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