Asked by sophie
Solve the integral
∫csc(z+π/6)cot(z+π/6)dz
∫csc(z+π/6)cot(z+π/6)dz
Answers
Answered by
Steve
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
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