Find the integral?

Question

Find the integral of (tan θ-1)^2 dθ. 

 

Answer: tan θ+2*ln abs(cos θ)+C

where abs means absolute value.

 

Please show all your work. 

Answer 1

Hey Sun,

         Hint expand the integrand to tan²θ - 2tanθ +1 and integrate term by term and recall that 

tan² = sec² -1 and I think you can work it out.

 

Jim