Not a homework question, a test question that I already took.

After the test it suddenly hit me that I can convert it into Csc^2 but I did it in a totally convoluted way on the test

can someone check whether I’m right.

I did it via integration by parts

u=cot^2

du=2cot csc^2

dv=1

v=x

so xcot^2 - 2Sxcot(csc^2)dx

second integration by parts

u=x

du=1

dv=cot(csc^2)

v= S cot(csc^2)

I made u one csc, and du csc(cot), and I inverted the preceding sign.

By now it’s too hard to organize it in a textbook or transcribe it from paper so whatever answer I got from the above is what I got on the test. Maybe I commited an arithmetic error (like - instead of + in one or more instances but I won’t lose all credit for that)

Was at least my procedure correct?

Something tells me I’m not allowed to use the Power Rule with squares of trignometric functions but I hope I’m wrong.