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sin^6x*cosxdx

Integral of sin^6x*cosxdx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                  
  /                  
 |                   
 |     6             
 |  sin (x)*cos(x) dx
 |                   
/                    
0                    
$$\int\limits_{0}^{1} \sin^{6}{\left(x \right)} \cos{\left(x \right)}\, dx$$
Integral(sin(x)^6*cos(x), (x, 0, 1))
Detail solution
  1. Let .

    Then let and substitute :

    1. The integral of is when :

    Now substitute back in:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                               
 |                            7   
 |    6                    sin (x)
 | sin (x)*cos(x) dx = C + -------
 |                            7   
/                                 
$$\int \sin^{6}{\left(x \right)} \cos{\left(x \right)}\, dx = C + \frac{\sin^{7}{\left(x \right)}}{7}$$
The graph
The answer [src]
   7   
sin (1)
-------
   7   
$$\frac{\sin^{7}{\left(1 \right)}}{7}$$
=
=
   7   
sin (1)
-------
   7   
$$\frac{\sin^{7}{\left(1 \right)}}{7}$$
sin(1)^7/7
Numerical answer [src]
0.0426752405751304
0.0426752405751304
The graph
Integral of sin^6x*cosxdx dx

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