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cos^3xsinx

Integral of cos^3xsinx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                  
  /                  
 |                   
 |     3             
 |  cos (x)*sin(x) dx
 |                   
/                    
0                    
$$\int\limits_{0}^{1} \sin{\left(x \right)} \cos^{3}{\left(x \right)}\, dx$$
Integral(cos(x)^3*sin(x), (x, 0, 1))
Detail solution
  1. There are multiple ways to do this integral.

    Method #1

    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:

    Method #2

    1. Rewrite the integrand:

    2. Let .

      Then let and substitute :

      1. Integrate term-by-term:

        1. The integral of a constant is the constant times the variable of integration:

        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:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                               
 |                            4   
 |    3                    cos (x)
 | cos (x)*sin(x) dx = C - -------
 |                            4   
/                                 
$$-{{\cos ^4x}\over{4}}$$
The graph
The answer [src]
       4   
1   cos (1)
- - -------
4      4   
$${{1}\over{4}}-{{\cos ^41}\over{4}}$$
=
=
       4   
1   cos (1)
- - -------
4      4   
$$- \frac{\cos^{4}{\left(1 \right)}}{4} + \frac{1}{4}$$
Numerical answer [src]
0.228694717720381
0.228694717720381
The graph
Integral of cos^3xsinx dx

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