Solving Integral of csc^3(x)cot(x)

[ludi_srbin]

Homework Statement

integral of csc^3(x)cot(x)

Homework Equations

I tried using trig identity 1+cot^2(x)=csc^2(x) but I got result where I canceled my indegrals.

The Attempt at a Solution

I tried to substitute the above mentioned indentity for csc^2 but I end up getting -cscx + intgr. cscxcot^3(x). I then substituted for cot^2 but then got to the point where I had -cscx + intgr. csc^(3)xcotx + cscx. At this point everything canceled out. I also tried substituting sin and cos in the original equation but that didn't get me anywhere neither.

 

[d_leet]

Try splitting csc³(x)cot(x) into csc²(x)*(csc(x)cot(x)) does that help at all?

 

[mjsd]

write out $$\csc^3 (x), \cot(x)$$ in terms of $$\cos(x), \sin(x)$$ and use subsitution or do by inspection

 

[HallsofIvy]

d_leet's suggestion is simpler (what is the derivative of csc(x)?) while mjsd's suggestion is more "fundamental" (you don't need to know the derivatiive of csc(x), only of cos(x)) but they both give the correct answer.