# How would I integrate this?

Describe the method you would use to integrate

cot^a(x) csc^b(x) dx

If a and b are odd?

An explanation of the strategy would be a huge help!

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I would definitely try to put everything into terms of sin and cos.

cot^a(x) = Cos^a(x) / sin^a(x)

csc^b(x) = 1/sin^b(x)

this is where i would start. from there, you can sum the powers of the sin's in the denominators and try u substitution or something.

Mark44
Mentor
Describe the method you would use to integrate

cot^a(x) csc^b(x) dx

If a and b are odd?

An explanation of the strategy would be a huge help!
Take out one factor each of csc x and cot x, leaving you with
$$\int cot^{a-1}(x)csc^{b - 1}(x)~csc(x)cot(x)dx$$

Use the identity cot2(x) + 1 = csc2(x) (or equivalently, cot2(x) = csc2(x) - 1) to replace the cota - 1 factor.

At that point you'll have a sum of terms that involve various powers of csc2(x) and you can use an ordinary substitution, with u = csc(x).