Solve the integral

Question

∫csc(z+π/6)cot(z+π/6)dz

Answer 1

Recall that the derivative of cscx is -cscx * cot x
so the answer is -csc(z+π/6)

Or, if you like pain, let u = x+π/6 and you have

∫ cscu cotu dz
∫ cosu/sin^2 u du

Now if v=sinu, you have

∫ v^-2 dv
= -1/v
= -1/sinu
= -csc(z+π/6) + C