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sin^2x*cosxdx
Solving integrals/ sin^2x*cosxdx

Integral of sin^2x*cosxdx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  2                    
 e                     
  /                    
 |                     
 |     2               
 |  sin (x)*cos(x)*1 dx
 |                     
/                      
e
$$\int\limits_{e}^{e^{2}} \sin^{2}{\left(x \right)} \cos{\left(x \right)} 1\, dx$$ 
Integral(sin(x)^2*cos(x)*1, (x, E, exp(2)))
Detail solution

  1. Let .

    Then let and substitute :

    1. The integral of is when :

    Now substitute back in:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                 
 |                              3   
 |    2                      sin (x)
 | sin (x)*cos(x)*1 dx = C + -------
 |                              3   
/
$${{\sin ^3x}\over{3}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
     3         3/ 2\
  sin (e)   sin \e /
- ------- + --------
     3         3
$${{\sin ^3e^2}\over{3}}-{{\sin ^3E}\over{3}}$$ 
=
= 
     3         3/ 2\
  sin (e)   sin \e /
- ------- + --------
     3         3
$$- \frac{\sin^{3}{\left(e \right)}}{3} + \frac{\sin^{3}{\left(e^{2} \right)}}{3}$$
Simplify
Numerical answer [src] 
0.214951169522454
0.214951169522454
The graph
Integral of sin^2x*cosxdx dx

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

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