How Can You Integrate Cot^6(x) Without Using the Reduction Formula?

[rdioface]

Homework Statement

Find the integral of cot^6(x) without using the reduction formula.

Homework Equations

Potentially any trig identities involving the cotangent

The Attempt at a Solution

I tried splitting up the cot^6 in various ways such as cot^4*cot^2 and cot^2*cot^2*cot*2 but nothing has produced a solution, nor has doing a similar splitting and integrating by parts.

 

[Mark44]

Homework Statement

Find the integral of cot^6(x) without using the reduction formula.

Homework Equations

Potentially any trig identities involving the cotangent

The Attempt at a Solution

I tried splitting up the cot^6 in various ways such as cot^4*cot^2 and cot^2*cot^2*cot*2 but nothing has produced a solution, nor has doing a similar splitting and integrating by parts.

Use the identity cot^2(x) = csc^2(x) - 1 to write cot^6(x) as cot^4(x)(csc^2(x) - 1). Expanding this gives you cot^4(x) * csc^2(x) - cot^4(x).

In the first term, let u = cot(x), so du = -csc^2(x). For the second term, use the same trick again.

 

[rdioface]

Danke schoen!