Question

Another question dealing heavily with Indefinite Integrals and Anti-Derivitaives!
The problem: Evaluate the following integral using U Substitution– "integral[(csc^2(2theta))(cot(2theta))(dtheta)]" ...
a) solve using: "u = cot(2theta)"
b) solve using: "u = csc(2theta)"

Any and all help is greatly appreciated! :)

Answer 1

case a) if you set u = cot(2theta) what will your du be?

Answer 2

-csc(2theta)(dtheta)

Answer 3

You need to use chainrule for that, so it'll actually be
u = cot(2theta)
du = -csc^2(2theta)(dtheta)
So now, knowing this what will the original dtheta equal?

Answer 4

du = -csc^2(2theta)(dtheta)*2, my bad :D

Answer 5

dtheta = du/-csc^2(2theta))

Answer 6

Right, so it will simplify to