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(cos(2x))/(sin^3(2x))

Integral of (cos(2x))/(sin^3(2x)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1             
  /             
 |              
 |   cos(2*x)   
 |  --------- dx
 |     3        
 |  sin (2*x)   
 |              
/               
0               
$$\int\limits_{0}^{1} \frac{\cos{\left(2 x \right)}}{\sin^{3}{\left(2 x \right)}}\, dx$$
Integral(cos(2*x)/sin(2*x)^3, (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. Let .

        Then let and substitute :

        1. The integral of is when :

        Now substitute back in:

      So, the result is:

    Now substitute back in:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                              
 |                               
 |  cos(2*x)               1     
 | --------- dx = C - -----------
 |    3                    2     
 | sin (2*x)          4*sin (2*x)
 |                               
/                                
$$\int \frac{\cos{\left(2 x \right)}}{\sin^{3}{\left(2 x \right)}}\, dx = C - \frac{1}{4 \sin^{2}{\left(2 x \right)}}$$
The graph
The answer [src]
oo
$$\infty$$
=
=
oo
$$\infty$$
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Numerical answer [src]
1.14420629737936e+37
1.14420629737936e+37
The graph
Integral of (cos(2x))/(sin^3(2x)) dx

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