Integrate by parts using the formula , where and .

Combine and .

Move to the left of .

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

Multiply by .

Let . Find .

Differentiate .

By the Sum Rule, the derivative of with respect to is .

Evaluate .

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

Differentiate using the Power Rule which states that is where .

Multiply by .

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.

Combine and .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

The integral of with respect to is .

Simplify.

Replace all occurrences of with .

Evaluate integral of arctan(4x) with respect to x