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Similar expressions
cos(x)*sin^4(x)

Integral of cosxsin^4x dx

The solution

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 |            4      
 |  cos(x)*sin (x) dx
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0

$$\int\limits_{0}^{0} \sin^{4}{\left(x \right)} \cos{\left(x \right)}\, dx$$

Integral(cos(x)*sin(x)^4, (x, 0, 0))

Detail solution

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

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

$\int u^{4}\, du$
1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int u^{4}\, du = \frac{u^{5}}{5}$
Now substitute $u$ back in:

$\frac{\sin^{5}{\left(x \right)}}{5}$
Add the constant of integration:

$\frac{\sin^{5}{\left(x \right)}}{5}+ \mathrm{constant}$

The answer is:

$\frac{\sin^{5}{\left(x \right)}}{5}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               
 |                            5   
 |           4             sin (x)
 | cos(x)*sin (x) dx = C + -------
 |                            5   
/

$$\int \sin^{4}{\left(x \right)} \cos{\left(x \right)}\, dx = C + \frac{\sin^{5}{\left(x \right)}}{5}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$0$$

Numerical answer [src]

0.0

0.0

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

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Identical expressions

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Integral of cosxsin^4x dx

Limits of integration:

The graph:

Piecewise:

The solution