Question

`\int\limits sec^(2)x`
`dx`
`=`

(AP Calculus AB)

Answer 1

The problem wishes us to integrate
`sec^(2)(x)`

-However, we know based on the derivation of tan (x)

`(d)/(dx)tan(x)=sec^(2) (x)`

Bascially integration is the reversal of the derivation:

Thus

`\int\limits^a_b {sec^(2)(x)} \, dx =tan(x) +C`

Since there are no bounds, we must add a constant 'C' as we don't know if there was an initial value

Hope that helps!