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Integral of 3sin^2x*cosxdx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
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 |  3*sin (x)*cos(x) dx
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$$\int\limits_{0}^{\frac{\pi}{2}} 3 \sin^{2}{\left(x \right)} \cos{\left(x \right)}\, dx$$
Integral((3*sin(x)^2)*cos(x), (x, 0, pi/2))
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]
  /                                 
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 |      2                       3   
 | 3*sin (x)*cos(x) dx = C + sin (x)
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$$\int 3 \sin^{2}{\left(x \right)} \cos{\left(x \right)}\, dx = C + \sin^{3}{\left(x \right)}$$
The graph
The answer [src]
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$$1$$
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$$1$$
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Numerical answer [src]
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    Use the examples entering the upper and lower limits of integration.