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

1 Answer
Jim H
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.

Related questions
See all questions in Integration by Parts
Impact of this question
1674 views around the world
You can reuse this answer
Creative Commons License