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Integral of sinx^2*cosx dx

The solution

You have entered [src]

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

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

Integral(sin(x)^2*cos(x), (x, 0, oo))

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

$$\int \sin^{2}{\left(x \right)} \cos{\left(x \right)}\, dx = C + \frac{\sin^{3}{\left(x \right)}}{3}$$

Simplify

The answer [src]

<-1/3, 1/3>

$$\left\langle - \frac{1}{3}, \frac{1}{3}\right\rangle$$

<-1/3, 1/3>

$$\left\langle - \frac{1}{3}, \frac{1}{3}\right\rangle$$

AccumBounds(-1/3, 1/3)

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

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Integral of sinx^2*cosx dx

Limits of integration:

The graph:

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The solution