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

Method: a^(nx) Antiderivative

Step 1: Simplify and look for algebraic rewrites.

This is your new version of Option 1 from limits. This means it is the first thing you will always want to do before you start actually applying a derivative rule. You must ensure that the equation is ready to have a derivative taken.

          Roots or Radicals

          x’s on the bottom of a fraction.

          Trig functions raised to a power.

Step 2: Identify any term(s) that includes the base case a ( n x ) .

Break the problem down into bitesize chunks based upon the + and , and identify the antiderivative rule for each chunk (term).

Each term should be thought of as its own small little problem.

Step 3: Take the antiderivativeof the base case a ( n x ) using its specific Recipe.

Step 4 ( Definite Integral ONLY ): Evaluate the antiderivative result using the TopBottom method.

Plug the upper bound into your antiderivative and subtract off the lower bound plugged into your antiderivative.

a b f ( x ) dx = F ( x ) | x = a x = b = F ( b ) F ( a )

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