Answer
$tan(t) + sec(t) + C $
Work Step by Step
We can multiply the outer term in the integral $sec (t) $ with the inner sum $sec(t) + tan (t) $ and integrate their products.
Our new integral is$ \int sec^2(t) + sec(t)tan(t) dt$
We use the trigonometric integral formulas $$ \frac{d}{dt}tan(t) = sec^2(t)$$
and $$ \frac{d}{dt}sec(t) = sec(t)tan(t)$$
to integrate and get the result
$tan(t) + sec(t) + C $
*Note the constant $C$ must be included due to the indefinite integral
