Trig Integration Problem: Integral of (sin(x))^3/tan(x)

To find the following indefinite integral:

May be written as: Integrate or integral of (Sin(x))^3/(tan(x)) or Integrate or integral of (sin(x))^3/tan(x)

Follow these steps:

  

We are trying to get this into a form where we can do u substitution. This is done by using trig identities and rewriting the integral.
First, rewrite this a (sin(x))^3/1 divided by sin(x)/cos(x):
Simplified from above:
Simplified further by dividing the sin(x) we now have this simplified integral:
Substitution can now be used. We see that if we let u=sin(x) this makem du=cos(x)dx. This takes care of the sin and the cos.
The integral rewritten with the u substitution:
Performing the integration with respect to u:
Now replacing our u with the value we specified above gives us our final answer of (1/3)(sin(x))^3 + C.