Calculus
Hello,
I'm having trouble with this exercise. Can you help me?
Integral of (x* (csc x)^2)dx
I'm using the uv  integral v du formula. I tried with u= (csc x)^2 and used some trigonometric formulas, but the expression became too complicated, I couldn't continue working. Then I tried with u=x, but the same happened.
Thank you in advance.
You are on the right track using integration by parts. Let u = x and let dv = csc^2 x dx = (1/sin^2 x) dx
du = x
v = cot x (You will have to prove that to yourself)
Integral u dv = uv  Integal v du
=  cot x  Integral (cot x dx)
=  cot x + log sin x
You will have to prove that Integral of cot x dx yourself also.
I have verified the steps and final answer with a table of integrals
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