Maybe try the identity
Im ok with Integration by inspection but cant get this example, see what you think…
∫ cot^2 (2x) dx with limits (π/4) and (π/8)
This is what I get
(-1/2 cot (2x) – x) with limits
(-1/2 (1/tan (π/2)) – π/4) – (-1/2 (1/tan (π/4)) – π/8)
But clearly it is impossible and a math error to have tan π/2 or 90° so im not sure how to progress from there. The answer in the book is (4 – π)/8.
Thanks for any help!