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Identical expressions
cos(x)*sin^ four (x)
co sinus of e of (x) multiply by sinus of to the power of 4(x)
co sinus of e of (x) multiply by sinus of to the power of four (x)
cos(x)*sin4(x)
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cos(x)*sin⁴(x)
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Similar expressions
cosx*sin^4(x)

Solving integrals/ cos(x)*sin^4(x)

Integral of cos(x)*sin^4(x) dx

The solution

You have entered [src]

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

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

Simplify

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   
/

$${{\sin ^5x}\over{5}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

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

$${{\sin ^51}\over{5}}$$

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

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

Simplify

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

Similar expressions

Integral of cos(x)*sin^4(x) dx

Limits of integration:

The graph:

Piecewise:

The solution