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Identical expressions
sin^22x×cosx
sinus of squared 2x× co sinus of e of x
sin22x×cosx
sin²2x×cosx
sin to the power of 22x×cosx
sin^22x×cosxdx

Solving integrals/ sin^22x×cosx

Integral of sin^22x×cosx dx

The solution

You have entered [src]

  1                   
  /                   
 |                    
 |     22             
 |  sin  (x)*cos(x) dx
 |                    
/                     
0

$$\int\limits_{0}^{1} \sin^{22}{\left(x \right)} \cos{\left(x \right)}\, dx$$

Integral(sin(x)^22*cos(x), (x, 0, 1))

Detail solution

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

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

$\int u^{22}\, du$
1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int u^{22}\, du = \frac{u^{23}}{23}$
Now substitute $u$ back in:

$\frac{\sin^{23}{\left(x \right)}}{23}$
Add the constant of integration:

$\frac{\sin^{23}{\left(x \right)}}{23}+ \mathrm{constant}$

The answer is:

$\frac{\sin^{23}{\left(x \right)}}{23}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                 
 |                             23   
 |    22                    sin  (x)
 | sin  (x)*cos(x) dx = C + --------
 |                             23   
/

$$\int \sin^{22}{\left(x \right)} \cos{\left(x \right)}\, dx = \frac{\sin^{23}{\left(x \right)}}{23} + C$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

   23   
sin  (1)
--------
   23

$${{\sin ^{23}1}\over{23}}$$

   23   
sin  (1)
--------
   23

$$\frac{\sin^{23}{\left(1 \right)}}{23}$$

Simplify

Numerical answer [src]

0.000820677466522084

0.000820677466522084

The graph

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

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Identical expressions

Integral of sin^22x×cosx dx

Limits of integration:

The graph:

Piecewise:

The solution