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 the factors of .

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.

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 .

Add and .

Rewrite the problem using and .

The integral of with respect to is .

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

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 .

Add and .

Rewrite the problem using and .

The integral of with respect to is .

Simplify.

Replace all occurrences of with .

Replace all occurrences of with .

Evaluate integral of (x+4)/(x^2+5x-6) with respect to x