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sin^3xcos^2xdx

Integral of sin^3xcos^2xdx dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                     
  /                     
 |                      
 |     3       2        
 |  sin (x)*cos (x)*1 dx
 |                      
/                       
0                       
$$\int\limits_{0}^{1} \sin^{3}{\left(x \right)} \cos^{2}{\left(x \right)} 1\, dx$$
Integral(sin(x)^3*cos(x)^2*1, (x, 0, 1))
Detail solution
  1. Rewrite the integrand:

  2. There are multiple ways to do this integral.

    Method #1

    1. Let .

      Then let and substitute :

      1. Integrate term-by-term:

        1. The integral of is when :

        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:

        The result is:

      Now substitute back in:

    Method #2

    1. Rewrite the integrand:

    2. Integrate term-by-term:

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

        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:

        So, the result is:

      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:

      The result is:

    Method #3

    1. Rewrite the integrand:

    2. Integrate term-by-term:

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

        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:

        So, the result is:

      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:

      The result is:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                            
 |                               3         5   
 |    3       2               cos (x)   cos (x)
 | sin (x)*cos (x)*1 dx = C - ------- + -------
 |                               3         5   
/                                              
$${{3\,\cos ^5x-5\,\cos ^3x}\over{15}}$$
The graph
The answer [src]
        3         5   
2    cos (1)   cos (1)
-- - ------- + -------
15      3         5   
$${{3\,\cos ^51-5\,\cos ^31}\over{15}}+{{2}\over{15}}$$
=
=
        3         5   
2    cos (1)   cos (1)
-- - ------- + -------
15      3         5   
$$- \frac{\cos^{3}{\left(1 \right)}}{3} + \frac{\cos^{5}{\left(1 \right)}}{5} + \frac{2}{15}$$
Numerical answer [src]
0.0899661660972821
0.0899661660972821
The graph
Integral of sin^3xcos^2xdx dx

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