Factor out of .

Raise to the power of .

Factor out of .

Factor out of .

Write the fraction using partial fraction decomposition.

Simplify.

Split the single integral into multiple integrals.

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 .

Multiply and .

Move to the left of .

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

The integral of with respect to is .

Simplify.

Replace all occurrences of with .

Evaluate integral of 1/(x^3+x) with respect to x