# Calculus Examples

Factor the numerator and denominator of .

Write as .

Replace each of the partial fraction coefficients with the actual values.

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 .

Multiply and to get .

Simplify the expression.

Move to the left of the expression .

Multiply by to get .

Since is constant with respect to , the integral of with respect to is .

Multiply and to get .

Multiply by to get .

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 to get .

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 to get .

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, .

Rewrite as a product.

Simplify by moving inside the logarithm.

Apply the product rule to .

Simplify the numerator.

Apply the product rule to .

Multiply the exponents in .

Reorder terms.