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

Integrate by parts using the formula , where and .
Simplify.
Combine and .
Move to the left of .
Since is constant with respect to , move out of the integral.
Multiply by .
Let . Then , so . Rewrite using and .
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 .
Rewrite the problem using and .
Simplify.
Multiply and .
Move to the left of .
Since is constant with respect to , move out of the integral.
Simplify.
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

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