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Solving integrals/ 4*sin^3x*cosx

Integral of 4*sin^3x*cosx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  x                    
  -                    
  3                    
  /                    
 |                     
 |       3             
 |  4*sin (x)*cos(x) dx
 |                     
/                      
x                      
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4
$$\int\limits_{\frac{x}{4}}^{\frac{x}{3}} 4 \sin^{3}{\left(x \right)} \cos{\left(x \right)}\, dx$$ 
Integral((4*sin(x)^3)*cos(x), (x, x/4, x/3))
Detail solution

  1. Let .

    Then let and substitute :

    1. The integral of a constant times a function is the constant times the integral of the function:

      1. The integral of is when :

      So, the result is:

    Now substitute back in:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                 
 |                                  
 |      3                       4   
 | 4*sin (x)*cos(x) dx = C + sin (x)
 |                                  
/
$$\int 4 \sin^{3}{\left(x \right)} \cos{\left(x \right)}\, dx = C + \sin^{4}{\left(x \right)}$$
Simplify
The answer [src] 
   4/x\      4/x\
sin |-| - sin |-|
    \3/       \4/
$$- \sin^{4}{\left(\frac{x}{4} \right)} + \sin^{4}{\left(\frac{x}{3} \right)}$$ 
=
= 
   4/x\      4/x\
sin |-| - sin |-|
    \3/       \4/
$$- \sin^{4}{\left(\frac{x}{4} \right)} + \sin^{4}{\left(\frac{x}{3} \right)}$$ 
sin(x/3)^4 - sin(x/4)^4

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

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