Integral of ex

How to solve the given integral by using the integral of ex: formula, 1 example, and its solution.

Formula

Formula

Recall that
the derivative of ex is itself: ex.

And integral and derivative
are the opposite operations.

So the integral of ex is also itself:
ex + C.

For an indefinite integral,
there should be +C.

Example

Example

Solution

e2x - 1
= [ex]2 - 12
= (ex + 1)(ex - 1)

Factor the Difference of Two Squares: a2 - b2

Cancel the factors (ex - 1).

The integral of ex is itself: ex.

The integral of +1 is +x.

Integral of a Polynomial

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

So ex + x + C is the answer.