What is the integral of (arctan(x))/x ?

The integral of (arctan(x))/x is 1/2 i(\Li_{2}(-ix)-\Li_{2}(ix))+C

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integral of (arctan(x))/x

\int \frac{arctan ( x )}{x} d x

\frac{1}{2} i (Li_{2} (- i x) - Li_{2} (i x)) + C

Solution steps

\int \frac{arctan ( x )}{x} d x

Use the nonelementary integral:

\int \frac{arctan ( x )}{x} d x = \frac{1}{2} i (Li_{2} (- i x) - Li_{2} (i x))

= \frac{1}{2} i (Li_{2} (- i x) - Li_{2} (i x))

Add a constant to the solution

= \frac{1}{2} i (Li_{2} (- i x) - Li_{2} (i x)) + C

\int \frac{6 ln ( x )}{x} d x

\frac{d}{d x} (\frac{1}{9 + x ^{2}})

\int x^{2} (1 - x)^{5} d x

\int \frac{x ^{3}}{x ^{2} + 2 x + 5} d x

\frac{d}{d t} (- e^{- t^{2}})

What is the integral of (arctan(x))/x ?
The integral of (arctan(x))/x is 1/2 i(\Li_{2}(-ix)-\Li_{2}(ix))+C