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

y \to \infty lim (\frac{y ^{2} + 2}{5 y - 6})

x \frac{d y}{d x} - y = 7 x^{3}

\int x + 2 d x

\int 3 e d x

\frac{\partial}{\partial x} (sin^{4} (x - 7 y))

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