Question

∫tanx

Answer 1

∫ tan(x) dx = ∫ sin(x)/cos(x) dx =
Let cos(x) = u
-sin(x) dx = du
sin(x) dx = -du
The integral becomes

- ∫ du/u = -ln|u| = - ln |cos(x)| + C

You do not have a negative sign in your answer.

Answer 2

oh i see thanks:)