# Calculus Examples

Factor the numerator and denominator of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor by grouping.
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
Factor out of .
Rewrite as plus
Apply the distributive property.
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
Factor out the greatest common factor (GCF) from each group.
Factor the polynomial by factoring out the greatest common factor, .
Write the fraction using partial fraction decomposition.
Simplify.
Split the single integral into multiple integrals.
Since is constant with respect to , move out of the integral.
The integral of with respect to is .
Since is constant with respect to , move out of the integral.
Let . Then , so . Rewrite using and .
Let . Find .
Rewrite.
Divide by .
Rewrite the problem using and .
Simplify.
Multiply and .
Move to the left of .
Since is constant with respect to , move out of the integral.
Simplify.
Multiply and .
Multiply by .
The integral of with respect to is .
Since is constant with respect to , move out of the integral.
Since is constant with respect to , move out of the integral.
Let . Then . Rewrite using and .
Let . Find .
Differentiate .
By the Sum Rule, the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Since is constant with respect to , the derivative of with respect to is .