MathAnalysisCalculusIntegrals

Integration by parts

What is the antiderivative?

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What is does the following integral evaluate to?

$\int \arctan(2x) dx$

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x \arctan(2x) - \frac{1}{4} \ln | 1 + 4x^2 | + C

2x \arctan(2x) - \frac{1}{2} \ln | 1 + 4x^2 | + C

\frac{x \arctan(2x)}{2} - \frac{1}{4} \ln | 1 + 4x^2 | + C

x \arctan(2x) - \frac{1}{2} \ln | 1 + 2x^2 | + C

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