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.