Question

How do you integrate `tanx * sec^3x dx`?

Answer 1

`1/3sec^3x+C`

Explanation:

We have:

`inttanxsec^3xdx`

Notice that we can write this in terms of `secx` and the derivative of `secx`, which is `secxtanx`.

Make the substitution `u=secx`, implying that `du=secxtanxdx`.

We can rewrite the integral as such:

`=intsec^2x(secxtanxdx)=intu^2du=1/3u^3+C=1/3sec^3x+C`