Question

What is the antiderivative of `secx`?

Answer 1

To find the antiderivative (or integral), there is a trick to this.

`intsecxdx`

You can multiply by `(secx + tanx)/(secx + tanx)`.

`= int(secx(secx + tanx))/(secx + tanx)dx`

`= int(sec^2x + secxtanx)/(secx + tanx)dx`

Now if you let:
`u = secx + tanx`
`du = secxtanx + sec^2xdx`

then you get:

`= int1/udu`

`= ln|u| + C`

`= ln|secx + tanx| + C`