Integral of e^x

Recall that
the derivative of e^x is itself: e^x.

And integral and derivative
are the opposite operations.

So the integral of e^x is also itself:
e^x + C.

For an indefinite integral,
there should be +C.

e^2x - 1
= [e^x]² - 1²
= (e^x + 1)(e^x - 1)

Factor the Difference of Two Squares: a² - b²

Cancel the factors (e^x - 1).

The integral of e^x is itself: e^x.

The integral of +1 is +x.

Integral of a Polynomial

The given integral is an indefinite integral.
So write +C.

So e^x + x + C is the answer.