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)

         $\frac{d}{dx}tan(x)=sec^{2} (x)$

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!