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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integral of arctan(x)

\int arctan (x) d 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

= 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

cos^{2} (t) \frac{d y}{d t} = 1

\frac{d}{d x} (\frac{3 x - 1}{x})

\frac{\partial}{\partial x} (2 x^{2} + 3 y^{2})

\frac{d ^{2}}{d x ^{2}} (x^{2})

\int_{0}^{16} sin (x) d x

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