How do you integrate int x^2 csc ^2 x^2 dx using integration by parts?

1 Answer
Jan 17, 2016

I don't believe that you do. Wolfram Alpha gives "no result found in terms of standard mathematics functions"

Explanation:

Perhaps if the integrand were x^3csc^2(x^2)

Clearly choosing u = csc^2(x^2) and dv = x^2 dx will not result in anything we can integrate.
(We get vdu involving x^4csc^2(x^2) cot(x^2), which is not promising.)

We can integrate x csc^2(x^2) by substitution, but our vdu involves just kint cot(x^2)dx, which does not look like something we can do.