Question

Find the integral of (tan(theta)-1)^2 d*theta.

Answer 1

@thomaster

Answer 2

\[\int (\tan\theta-1)^2~d\theta~~?\]
Expand the binomial:
\[(\tan\theta-1)^2=\color{red}{\tan^2\theta}-2\tan\theta\color{red}{+1}=\color{red}{\sec^2\theta}-2\tan\theta\]
(red indicates the use of an identity.
\[\int\sec^2\theta~d\theta-2\int\tan\theta~d\theta\\
\int\sec^2\theta~d\theta-2\int\frac{\sin\theta}{\cos\theta}~d\theta\]
First is easy, the second requires a substitution.