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

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