Question

integral of tanx???

Answer 1

Rewrite Tan as Sin/Cos

Answer 2

This is one of many known elementary forms.

The integral of tan(u)du = -ln|cos(u)| + C

Answer 3

Then let u = Cosx, du = -Sinx(dx)

Answer 4

Ahhh right. Good to know. Im doing a refresher Worksheet and that one slipped my mind. Thank you.

Answer 5

So
Int(Tanx) = Int(Sin/Cos) = Int(-du/u) = -ln|u| + C

Answer 6

which is what pompeii told you.

Answer 7

Or if you prefer a slightly different but equivalent form to Pompeii00 you can write it as:
\[\ln|\sec(u)| + C\] by using properties of logs.

Answer 8

I recall that ln(secx)+c and -ln(cosx)+c are equal. thank you!

Answer 9

So...?