Question

What's the integral of `(tanx)^2`?

Answer 1

It is

#int (tanx)^2dx=int (sin^2x)/cos^2xdx=int (1-cos^2x)/cos^2xdx= int 1/(cos^2x)dx-int 1dx=tanx-x+c#

where `c` is the integration constant

Note we used the following trigonometric identities

1) `tanx=sinx/cosx`

2) `sin^2x+cos^2x=1`