Question

AGAIN INTEGRATION ...

Answer 1

\[\int\limits_{}\tan ^{2}(2x-3)dx{}\]

Answer 2

Start off by using trigonometric identities:

tan^2x=sec^2x-1

Answer 3

then???

Answer 4

and I'm sure you can finish the rest from there!!
if you integrate sec^2x, you get tanx

Answer 5

but remember there is a linear function inside the trig function!

Answer 6

and if you integrate a constant, you get kx :) the rest should be easy!

The final answer should be:
-(x+1/2*tan(3-2x))

Answer 7

first, use int by u-sub
let u = 2x - 3
du = 2 dx
dx = 1/2 du

see your integration becomes
1/2 int (tan^2 (u)) du
= 1/2 int(sec^2 (u) - 1)
= 1/2 ( tan(u) - u) + c

dont forget : substitute back that u = 2x-3