Method: e^(x) Antiderivatives

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 $e^{\left(nx\right)}$.

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 $e^{\left(nx\right)}$ using its specific Recipe.

Step 4 ( Definite Integral ONLY ): Evaluate the antiderivative result using the Top – Bottom method.

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

$\underset{a}{\overset{b}{\int }}f\left(x\right)\mathit{dx}\mathit{=}{F\left(x\right)|}_{x=a}^{x=b}\mathit{=}F\left(b\right)–F\left(a\right)$