Integral of sin^4xcosx dx

The solution

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  1                  
  /                  
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 |     4             
 |  sin (x)*cos(x) dx
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0

$$\int\limits_{0}^{1} \sin^{4}{\left(x \right)} \cos{\left(x \right)}\, dx$$

Integral(sin(x)^4*cos(x), (x, 0, 1))

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)
 | sin (x)*cos(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]

   5   
sin (1)
-------
   5

$$\frac{\sin^{5}{\left(1 \right)}}{5}$$

   5   
sin (1)
-------
   5

$$\frac{\sin^{5}{\left(1 \right)}}{5}$$

sin(1)^5/5

Numerical answer [src]

0.0843773191639561

0.0843773191639561

The graph

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

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Identical expressions

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Integral of sin^4xcosx dx

Limits of integration:

The graph:

Piecewise:

The solution