Integrate by the function 2cosx/3sin²x

Answer 1

∫ 2cosx/3sin²x dx
= ∫ (2/3) cosx (sinx)^-2 dx

= (-2/3) (sinx)^-1 + c
or -2/(3sinx) + c
or (-2/3)csc x + c

I did it by inspection, noting the the derivative of the power sin^2 x showed up as the correct cosx in the product