Question

What is ∫tan^2 x dX ?

Answer 1

`I=tan(x)-x+C`

Explanation:

We want to solve

`I=inttan^2(x)dx`

Using the trig identity `color(blue)(tan^2(x)=sec^2(x)-1`

`I=intsec^2(x)-1dx`

Remember `color(blue)((tan(x))'=sec^2(x)`, thus

`I=tan(x)-x+C`