Question

How do you integrate `int secy(tany-secy)dy`?

Answer 1

`intsecy(tany-secy)dy`

`=int(secytany-sec^2y)dy`

`=intsecytanydy-intsec^2ydy`

Since `d/dysecy=secytany`, we see that `intsecytany=secy`. Similarly, since `d/dytany=sec^2y`, we see that `intsec^2ydy=tany`.

`=secy-tany+C`