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sinx*cos^6x*dx

Integral of sinx*cos^6x*dx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                    
  /                    
 |                     
 |            6        
 |  sin(x)*cos (x)*1 dx
 |                     
/                      
0                      
$$\int\limits_{0}^{1} \sin{\left(x \right)} \cos^{6}{\left(x \right)} 1\, dx$$
Integral(sin(x)*cos(x)^6*1, (x, 0, 1))
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]
  /                                 
 |                              7   
 |           6               cos (x)
 | sin(x)*cos (x)*1 dx = C - -------
 |                              7   
/                                   
$$\int \sin{\left(x \right)} \cos^{6}{\left(x \right)} 1\, dx = C - \frac{\cos^{7}{\left(x \right)}}{7}$$
The graph
The answer [src]
       7   
1   cos (1)
- - -------
7      7   
$$\frac{1}{7} - \frac{\cos^{7}{\left(1 \right)}}{7}$$
=
=
       7   
1   cos (1)
- - -------
7      7   
$$\frac{1}{7} - \frac{\cos^{7}{\left(1 \right)}}{7}$$
Numerical answer [src]
0.140936884309461
0.140936884309461
The graph
Integral of sinx*cos^6x*dx dx

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