# Integral of e^{x}

How to solve the given integral by using the integral of e^{x}: formula, 1 example, and its solution.

## Formula

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.

## Example∫ (e^{2x} - 1)/(e^{x} - 1) dx

Solution

Solution (Detail)

e^{2x} - 1

= [e^{x}]^{2} - 1^{2}

= (e^{x} + 1)(e^{x} - 1)

Factor the Difference of Two Squares: a^{2} - b^{2}

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.