U-Substitution to find indefinite integral

[kekjj]

The question I am working on states "Use a substitution to evaluate the following indefinite integrals". This should be u-substitution, since that is our most recent unit.


I understand that I should probably set the denominator to my u. let u = cot(x) - pi . then du/dx = -csc^2(x).

What comes after? My thought is to take the integral of (csc(x)/u)^2, which results in 1/3(csc(x)/cot(x) - pi) ^ 3. This doesn't seem right, as that completely ignores the du/dx calculated in the first step.

I'm not sure what the right approach is in this case.

 

[Dr.Peterson]

You want to express the integrand as the product of some function of u, and the differential [imath]du=\frac{du}{dx}dx[/imath]. You have the differential, [imath]-\csc^2(x)dx=du[/imath]; and you have a function [imath]\left(\frac{1}{\cot(x)-\pi}\right)^2=u^{-2}[/imath]. Put them together. (Note that the goal is an expression in u only, not in x!)

It may help if you show us an example of how your textbook expresses a substitution, so we can use the same style.