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

a ( nx )

Base Case: a ( nx )

Base Case

Definite Integral

Indefinite Integral

f ( x ) = a ( n x )

Where the a and the n are any number .

a b a ( n x )   dx = 1 ln ( a ) n a ( n x ) | x = a x = b

a ( n x )   dx = 1 ln ( a ) n a ( n x ) + C

Note :   As soon as whatever is inside the function, inside the parenthesis, is more than just your basic x , the problem’s primary method becomes a u-substitution .

I include the n in my base case because it is one of the most common ways you will see this special case presented, and by memorizing it this way you can save yourself an unnecessary u-substitution .

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