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cos2x/sin^2xdx

Integral of cos2x/sin^2x dx

The solution

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  0            
  /            
 |             
 |  cos(2*x)   
 |  -------- dx
 |     2       
 |  sin (x)    
 |             
/              
0

$$\int\limits_{0}^{0} \frac{\cos{\left(2 x \right)}}{\sin^{2}{\left(x \right)}}\, dx$$

Integral(cos(2*x)/sin(x)^2, (x, 0, 0))

Detail solution

Rewrite the integrand:

$\frac{\cos{\left(2 x \right)}}{\sin^{2}{\left(x \right)}} = \frac{2 \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{1}{\sin^{2}{\left(x \right)}}$
Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{2 \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\, dx = 2 \int \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\, dx$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $- x - \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$
  So, the result is: $- 2 x - \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \frac{1}{\sin^{2}{\left(x \right)}}\right)\, dx = - \int \frac{1}{\sin^{2}{\left(x \right)}}\, dx$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $- \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$
  So, the result is: $\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$
The result is: $- 2 x - \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$
Now simplify:

$- 2 x - \frac{1}{\tan{\left(x \right)}}$
Add the constant of integration:

$- 2 x - \frac{1}{\tan{\left(x \right)}}+ \mathrm{constant}$

The answer is:

$- 2 x - \frac{1}{\tan{\left(x \right)}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                              
 |                               
 | cos(2*x)                cos(x)
 | -------- dx = C - 2*x - ------
 |    2                    sin(x)
 | sin (x)                       
 |                               
/

$$\int \frac{\cos{\left(2 x \right)}}{\sin^{2}{\left(x \right)}}\, dx = C - 2 x - \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$0$$

Numerical answer [src]

0.0

0.0

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

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Identical expressions

Integral of cos2x/sin^2x dx

Limits of integration:

The graph:

Piecewise:

The solution