# Calculus Examples

Factor the numerator and denominator of .
Write as .
Simplify.
Rewrite as a product.
Multiply and .
Since integration is linear, the integral of with respect to is .
Since is constant with respect to , the integral of with respect to is .
The integral of with respect to is .
Since is constant with respect to , the integral of with respect to is .
Let . Then , so . Rewrite using and .
Combine fractions.
Multiply and .
Simplify the expression.
Move to the left of the expression .
Multiply by .
Since is constant with respect to , the integral of with respect to is .
Combine fractions.
Multiply and .
Multiply by .
The integral of with respect to is .
Since is constant with respect to , the integral of with respect to is .
Since is constant with respect to , the integral of with respect to is .
Remove parentheses around .
Let . Then . Rewrite using and .
The integral of with respect to is .
Simplify.
Write as a fraction with denominator .
Multiply and .
Replace all occurrences of with .
Replace all occurrences of with .
Use the product property of logarithms, .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify each term.
Simplify the numerator.
Simplify .
Apply the product rule to .
Multiply the exponents in .
Multiply the exponents in .
Simplify.
Use the quotient property of logarithms, .
Reorder terms.