Question

How do you find the antiderivative of `y=csc(x)cot(x)`?

Answer 1

We will use a u substitution

Start off by rewriting

`int(1/sinx)(cosx/sinx)dx`

`intcosx/sin^2xdx`

Let `u =sinx`

`du=cosxdx`

Now make the substitution

`int(du)/u^2=intu^-2du`

Integrating we get

`-1/u`

Now back substitute for u

`-1/sinx+C`

`-cscx+C`