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Solving integrals/ cosec^3*x

Integral of cosec^3*x dx

Limits of integration:

from to
v

The graph:

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Piecewise:

The solution

You have entered [src] 
  1           
  /           
 |            
 |     3      
 |  csc (x) dx
 |            
/             
0
∫01csc⁡3(x) dx\int\limits_{0}^{1} \csc^{3}{\left(x \right)}\, dx 
Integral(csc(x)^3, (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                    
 |                                                                     
 |    3             log(1 + cos(x))   log(-1 + cos(x))       cos(x)    
 | csc (x) dx = C - --------------- + ---------------- + --------------
 |                         4                 4                     2   
/                                                        -2 + 2*cos (x)
∫csc⁡3(x) dx=C+log⁡(cos⁡(x)−1)4−log⁡(cos⁡(x)+1)4+cos⁡(x)2cos⁡2(x)−2\int \csc^{3}{\left(x \right)}\, dx = C + \frac{\log{\left(\cos{\left(x \right)} - 1 \right)}}{4} - \frac{\log{\left(\cos{\left(x \right)} + 1 \right)}}{4} + \frac{\cos{\left(x \right)}}{2 \cos^{2}{\left(x \right)} - 2}
Simplify
The answer [src] 
     pi*I
oo + ----
      4
∞+iπ4\infty + \frac{i \pi}{4} 
=
= 
     pi*I
oo + ----
      4
∞+iπ4\infty + \frac{i \pi}{4} 
oo + pi*i/4
Numerical answer [src] 
9.15365037903492e+37
9.15365037903492e+37

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

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