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$a^{(nx)}$

Unit 6: Antiderivatives 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 .

$\int_{a}^{b} a^{(n x)} dx = {\frac{1}{\ln (a) n} a^{(n x)} |}_{x = a}^{x = b}$

$\int a^{(n x)} dx = \frac{1}{\ln (a) n} a^{(n x)} + C$

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 .