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

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 ${x}^{3} {\csc}^{2} \left({x}^{2}\right)$

Clearly choosing $u = {\csc}^{2} \left({x}^{2}\right)$ and $\mathrm{dv} = {x}^{2} \mathrm{dx}$ will not result in anything we can integrate.
(We get $v \mathrm{du}$ involving ${x}^{4} {\csc}^{2} \left({x}^{2}\right) \cot \left({x}^{2}\right)$, which is not promising.)

We can integrate $x {\csc}^{2} \left({x}^{2}\right)$ by substitution, but our $v \mathrm{du}$ involves just $k \int \cot \left({x}^{2}\right) \mathrm{dx}$, which does not look like something we can do.