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sin^5(x)cos(x)dx

Integral of sin^5(x)cos(x)dx dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                  
  /                  
 |                   
 |     5             
 |  sin (x)*cos(x) dx
 |                   
/                    
0                    
$$\int\limits_{0}^{1} \sin^{5}{\left(x \right)} \cos{\left(x \right)}\, dx$$
Integral(sin(x)^5*cos(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 is when :

      Now substitute back in:

    Method #2

    1. Rewrite the integrand:

    2. 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]
  /                               
 |                            6   
 |    5                    sin (x)
 | sin (x)*cos(x) dx = C + -------
 |                            6   
/                                 
$$\int \sin^{5}{\left(x \right)} \cos{\left(x \right)}\, dx = C + \frac{\sin^{6}{\left(x \right)}}{6}$$
The graph
The answer [src]
   6   
sin (1)
-------
   6   
$$\frac{\sin^{6}{\left(1 \right)}}{6}$$
=
=
   6   
sin (1)
-------
   6   
$$\frac{\sin^{6}{\left(1 \right)}}{6}$$
sin(1)^6/6
Numerical answer [src]
0.0591675548769536
0.0591675548769536
The graph
Integral of sin^5(x)cos(x)dx dx

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