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  • Integral of d{x}:
  • Integral of e^(x^2) Integral of e^(x^2)
  • Integral of sin(x)^3 Integral of sin(x)^3
  • Integral of √(x^2+1) Integral of √(x^2+1)
  • Integral of cos(5x) Integral of cos(5x)
  • Identical expressions

  • eight *sin^ three (x)*sin(x)
  • 8 multiply by sinus of cubed (x) multiply by sinus of (x)
  • eight multiply by sinus of to the power of three (x) multiply by sinus of (x)
  • 8*sin3(x)*sin(x)
  • 8*sin3x*sinx
  • 8*sin³(x)*sin(x)
  • 8*sin to the power of 3(x)*sin(x)
  • 8sin^3(x)sin(x)
  • 8sin3(x)sin(x)
  • 8sin3xsinx
  • 8sin^3xsinx
  • 8*sin^3(x)*sin(x)dx
  • Similar expressions

  • 8*sin^3(x)*sinx

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                   
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  |       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]
  /                                                                                                               
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 |      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)
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$$\int \sin{\left(x \right)} 8 \sin^{3}{\left(x \right)}\, dx = C + 3 x \sin^{4}{\left(x \right)} + 6 x \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)} + 3 x \cos^{4}{\left(x \right)} - 5 \sin^{3}{\left(x \right)} \cos{\left(x \right)} - 3 \sin{\left(x \right)} \cos^{3}{\left(x \right)}$$
The graph
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.