What is the integral of arctan(x) ?

The integral of arctan(x) is xarctan(x)-1/2 ln|x^2+1|+C

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Find the Antiderivative arctan(x)

integral

arctan (x)

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

Solution steps

\int arctan (x) d x

Apply Integration By Parts

= x arctan (x) - \int \frac{x}{x ^{2} + 1} d x

\int \frac{x}{x ^{2} + 1} d x = \frac{1}{2} ln x^{2} + 1

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

Add a constant to the solution

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

What is the integral of arctan(x) ?
The integral of arctan(x) is xarctan(x)-1/2 ln|x^2+1|+C