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

\frac{d}{d x} (cosh (ln (x)))

\int_{0}^{2} 6 d x

\int \frac{1}{x x - 1} d x

e^{- \frac{h}{7}}

\frac{d}{d x} (x \cdot e^{- x^{2}})

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