Find the integral

{eq}\displaystyle \int \arctan 4 x\ dx {/eq}.


Find the integral

{eq}\displaystyle \int \arctan 4 x\ dx {/eq}.

Integration by Parts:

We first recall the basic integration by parts formula:

{eq}\int u\, dv=uv-\int v\, du. {/eq}

The idea is to take an integral and call part of the integrand {eq}u {/eq} and the rest {eq}dV. {/eq} The rule of thumb is to pick something for {eq}u {/eq} whose derivative is not too complicated and something for {eq}dv {/eq} whose integral is not too complicated.

Answer and Explanation: 1

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We apply integration by parts.

{eq}\begin{align} \int \arctan (4x)\, dx &=\int \arctan (4x)\, dx & [\text{Use integration by parts with } u=\arctan...

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Learn more about this topic:

Using Integration By Parts


Chapter 13 / Lesson 7

Learn how to use and define integration by parts. Discover the integration by parts rule and formula. Learn when and how to use integration by parts with examples.

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