The Two Main Antiderivative Rules
Special Case Antiderivatives (The ones you have to memorize)
Initial Value Problems: Finding the +C
Fundamental Theorem of Calculus Part 1

x’s On the Bottom of a Fraction

Any time you see a number over a single x-value raised to a power, you will want to use this algebraic rewrite to bring that x up from the bottom of the fraction to the top.

Algebra: x’s on the bottom of a fraction



a x power

The a on top is any number.

a x power


Bring the x up from the bottom of the fraction to the top of the fraction and make the power negative.

5 x 3


5 x 3

7 8 x 5


The number, 8, is not attached to the x , it is a part of the fraction.

7 8 x 5

This example applies both the radical rewrite, and the x’s on the bottom of a fractionrewrite.

2 7   x 3 5


First, do the radical rewrite:

2 7 x 3 5

Then, do the x’s on the bottom of a fractionrewrite:

2 7 x 3 5


IMPORTANT : You will need to know this rewrite equally as well in both directions, left to right and right to left.

I always tell people negative exponents are great for doing calculus they SUCK for doing algebra.

Very often you will need to perform this rewrite once, left to right, while finding the antiderivative, and then again, right to left, when you start doing the algebra required in the application of that antiderivative.

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