Question

How do you integrate `secx^2/(1+tanx^2 )dx`?

Answer 1

The answer is `=x+C`

Explanation:

Let's do some simplification

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

Dividing by `cos^2x`

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

`tan^2x+1 =sec^2x`

So,

`int(sec^2xdx)/(1+tan^2x)`

`=int1*dx`

`=x+C`