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.