Question

Integrate([((Sqrt(Cot(x)))/(1+Cot(x)))],(0),(Pi/2))==Pi/4

Answer 1

Answer:

Step-by-step explanation:

This is not really one of that kind of integrals that Mathematica cannot handle with, but given

the case of a contest, how would we like to handle with it? I would like so much to know your ideas about tackling such integrals. Can we make things here really simple? Solutions are optional.

Calculate

∫π/40cot(x)cot2(x)+cot(x)−−−−−√dx

∫0π/4cot⁡(x)cot2⁡(x)+cot⁡(x)dx

Supplementary question: calculate

∫π/40xcot(x)cot2(x)+cot(x)−−−−−√dx.