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Solving integrals/ 1/(sin(2*x)*sin(x))

Integral of 1/(sin(2*x)*sin(x)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

  1. Rewrite the integrand:

  2. The integral of a constant times a function is the constant times the integral of the function:

    1. Don't know the steps in finding this integral.

      But the integral is

    So, the result is:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                                      
 |                                                                       
 |        1                    1       log(-1 + sin(x))   log(1 + sin(x))
 | --------------- dx = C - -------- - ---------------- + ---------------
 | sin(2*x)*sin(x)          2*sin(x)          4                  4       
 |                                                                       
/
$$\int \frac{1}{\sin{\left(x \right)} \sin{\left(2 x \right)}}\, dx = C - \frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{4} + \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{4} - \frac{1}{2 \sin{\left(x \right)}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
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Numerical answer [src] 
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    Use the examples entering the upper and lower limits of integration.

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