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Solving integrals/ cosxsin^2x

Integral of cosxsin^2x dx

The solution

You have entered [src]

  1                  
  /                  
 |                   
 |            2      
 |  cos(x)*sin (x) dx
 |                   
/                    
0

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

Simplify

Detail solution

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

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

$\int u^{2}\, du$
1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int u^{2}\, du = \frac{u^{3}}{3}$
Now substitute $u$ back in:

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                               
 |                            3   
 |           2             sin (x)
 | cos(x)*sin (x) dx = C + -------
 |                            3   
/

$${{\sin ^3x}\over{3}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

   3   
sin (1)
-------
   3

$${{\sin ^31}\over{3}}$$

   3   
sin (1)
-------
   3

$$\frac{\sin^{3}{\left(1 \right)}}{3}$$

Simplify

Numerical answer [src]

0.198607745530319

0.198607745530319

The graph

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

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Identical expressions

Similar expressions

Integral of cosxsin^2x dx

Limits of integration:

The graph:

Piecewise:

The solution