Integration By Substitution Problem (Trig)

[KingKai]

Homework Statement

Integrate the following using substitution techniques

∫e^3tcsc(e^3t)cot(e^3t) dt

Homework Equations

csc(t) = 1/sin(t)

cot(t) = 1/tan(t)

cot(t) = cos(t)/sin(t)

1 + cot²(t) = csc²(t)

The Attempt at a Solution

∫e^3tcsc(e^3t)cot(e^3t) dt

set u = cot(e^3t)

du = (3e^3t)(- csc²(e^3t)) dt


Make Substitution,


∫e^3tcsc(e^3t) (u) (1/(3e^3t)(- csc²(e^3t)) du



Whoops, csc does not cancel out..



My friend told me I had to make TWO substitutions, following this advice my head proceeded to explode.

After recollecting the pieces of my skull fragments and carefully gluing them together again, I posted this question.

 

[Mark44]

Homework Statement

Integrate the following using substitution techniques

∫e^3tcsc(e^3t)cot(e^3t) dt

Homework Equations

csc(t) = 1/sin(t)

cot(t) = 1/tan(t)

cot(t) = cos(t)/sin(t)

1 + cot²(t) = csc²(t)

The Attempt at a Solution

∫e^3tcsc(e^3t)cot(e^3t) dt

set u = cot(e^3t)

du = (3e^3t)(- csc²(e^3t)) dt


Make Substitution,


∫e^3tcsc(e^3t) (u) (1/(3e^3t)(- csc²(e^3t)) du



Whoops, csc does not cancel out..



My friend told me I had to make TWO substitutions, following this advice my head proceeded to explode.

After recollecting the pieces of my skull fragments and carefully gluing them together again, I posted this question.

I would be inclined to turn the cot and csc functions into their sine and cosine equivalents, and go from there.