# Calculus Examples

Factor the numerator and denominator of .
Factor using the AC method.
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Write the factored form using these integers.
Reorder terms.
Write the fraction using partial fraction decomposition.
Move the negative in front of the fraction.
Split the single integral into multiple integrals.
Since is constant with respect to , move out of the integral.
Let . Then . Rewrite using and .
The integral of with respect to is .
Since is constant with respect to , move out of the integral.
Let . Then . Rewrite using and .
The integral of with respect to is .
Simplify.
Replace all occurrences of with .
Replace all occurrences of with .