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xcosx/sin^3x

Integral of xcosx/sin^3x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  0            
  /            
 |             
 |  x*cos(x)   
 |  -------- dx
 |     3       
 |  sin (x)    
 |             
/              
0              
$$\int\limits_{0}^{0} \frac{x \cos{\left(x \right)}}{\sin^{3}{\left(x \right)}}\, dx$$
Detail solution
  1. Use integration by parts:

    Let and let .

    Then .

    To find :

    1. Let .

      Then let and substitute :

      1. The integral of is when :

      Now substitute back in:

    Now evaluate the sub-integral.

  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. Now simplify:

  4. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                      
 |                                       
 | x*cos(x)              x        cos(x) 
 | -------- dx = C - --------- - --------
 |    3                   2      2*sin(x)
 | sin (x)           2*sin (x)           
 |                                       
/                                        
$${{\left(2\,x\,\sin \left(2\,x\right)-\cos \left(2\,x\right)+1 \right)\,\sin \left(4\,x\right)+\left(\sin \left(2\,x\right)+2\,x\, \cos \left(2\,x\right)\right)\,\cos \left(4\,x\right)-4\,x\,\sin ^2 \left(2\,x\right)-\sin \left(2\,x\right)-4\,x\,\cos ^2\left(2\,x \right)+2\,x\,\cos \left(2\,x\right)}\over{\sin ^2\left(4\,x\right)- 4\,\sin \left(2\,x\right)\,\sin \left(4\,x\right)+\cos ^2\left(4\,x \right)+\left(2-4\,\cos \left(2\,x\right)\right)\,\cos \left(4\,x \right)+4\,\sin ^2\left(2\,x\right)+4\,\cos ^2\left(2\,x\right)-4\, \cos \left(2\,x\right)+1}}$$
The graph
The answer [src]
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Numerical answer [src]
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The graph
Integral of xcosx/sin^3x dx

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