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sin^4xcos^3xdx

Integral of sin^4xcos^3xdx dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                     
  /                     
 |                      
 |     4       3        
 |  sin (x)*cos (x)*1 dx
 |                      
/                       
0                       
$$\int\limits_{0}^{1} \sin^{4}{\left(x \right)} \cos^{3}{\left(x \right)} 1\, dx$$
Integral(sin(x)^4*cos(x)^3*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 a constant times a function is the constant times the integral of the function:

          1. The integral of is when :

          So, the result is:

        1. The integral of is when :

        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 is when :

          Now substitute back in:

        So, the result is:

      1. Let .

        Then let and substitute :

        1. The integral of is when :

        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 is when :

          Now substitute back in:

        So, the result is:

      1. Let .

        Then let and substitute :

        1. The integral of is when :

        Now substitute back in:

      The result is:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                            
 |                               7         5   
 |    4       3               sin (x)   sin (x)
 | sin (x)*cos (x)*1 dx = C - ------- + -------
 |                               7         5   
/                                              
$$-{{5\,\sin ^7x-7\,\sin ^5x}\over{35}}$$
The graph
The answer [src]
     7         5   
  sin (1)   sin (1)
- ------- + -------
     7         5   
$$-{{5\,\sin ^71-7\,\sin ^51}\over{35}}$$
=
=
     7         5   
  sin (1)   sin (1)
- ------- + -------
     7         5   
$$- \frac{\sin^{7}{\left(1 \right)}}{7} + \frac{\sin^{5}{\left(1 \right)}}{5}$$
Numerical answer [src]
0.0417020785888258
0.0417020785888258
The graph
Integral of sin^4xcos^3xdx dx

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