What is the integral of (arctan(1/x)) ?

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

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integral of (arctan(1/x))

\int (arctan (\frac{1}{x})) d x

x arctan (\frac{1}{x}) + \frac{1}{2} ln 1 + x^{2} + C

Solution steps

\int arctan (\frac{1}{x}) d x

Apply Integration By Parts

= x arctan (\frac{1}{x}) - \int - \frac{x}{1 + x ^{2}} d x

\int - \frac{x}{1 + x ^{2}} d x = - \frac{1}{2} ln 1 + x^{2}

= x arctan (\frac{1}{x}) - (- \frac{1}{2} ln 1 + x^{2})

Simplify

= x arctan (\frac{1}{x}) + \frac{1}{2} ln 1 + x^{2}

Add a constant to the solution

= x arctan (\frac{1}{x}) + \frac{1}{2} ln 1 + x^{2} + C

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