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  • Identical expressions

  • eight *sin^ three (x)*sin(x)
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  • Similar expressions

  • 8*sin^3(x)*sinx
Solving integrals/ 8*sin^3(x)*sin(x)

Integral of 8*sin^3(x)*sin(x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 2*pi                   
   /                    
  |                     
  |       3             
  |  8*sin (x)*sin(x) dx
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 /                      
 0
$$\int\limits_{0}^{2 \pi} \sin{\left(x \right)} 8 \sin^{3}{\left(x \right)}\, dx$$ 
Integral((8*sin(x)^3)*sin(x), (x, 0, 2*pi))
The answer (Indefinite) [src] 
  /                                                                                                               
 |                                                                                                                
 |      3                         3                  3                    4             4             2       2   
 | 8*sin (x)*sin(x) dx = C - 5*sin (x)*cos(x) - 3*cos (x)*sin(x) + 3*x*cos (x) + 3*x*sin (x) + 6*x*cos (x)*sin (x)
 |                                                                                                                
/
$$\int \sin{\left(x \right)} 8 \sin^{3}{\left(x \right)}\, dx = C + 3 x \sin^{4}{\left(x \right)} + 6 x \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)} + 3 x \cos^{4}{\left(x \right)} - 5 \sin^{3}{\left(x \right)} \cos{\left(x \right)} - 3 \sin{\left(x \right)} \cos^{3}{\left(x \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
6*pi
$$6 \pi$$ 
=
= 
6*pi
$$6 \pi$$ 
6*pi
Numerical answer [src] 
18.8495559215388
18.8495559215388

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

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