Question

How do you find the antiderivative of `1/(cos x)^2`?

Answer 1

Use `sec(x)=1/(cosx)` and rewrite as `intsec^2(x)`, where the anti-derivative of `sec^2x = tanx`.

Explanation:

This can also be written as:

`int1/(cosx)^2dx`

This one is a bit tricky in that you have to recognize that `1/cosx^2` is equivalent to `sec^2x`, but once you've figured that out, it's quite simple.

`=>intsec^2(x)dx`

The anti-derivative of `sec^2x` is simply `tan(x)`. We also account for any constants that could be present by adding a `+C` at the end of our answer. Thus,

`int1/(cosx)^2dx=intsec^2(x)dx = tan(x)+C`