Question

How do you integrate `int (tan^2y+1)dy`?

Answer 1

`tany+C`

Explanation:

Use the identity that comes from the Pythagorean Identity: `tan^2theta+1=sec^2theta`

Thus:

`int(tan^2y+1)dy=intsec^2ydy`

Since `d/dytany=sec^2y`, we see that:

`intsec^2ydy=tany+C`