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

= 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

\frac{d}{d x} (2 x^{2} - 4 x + 3)

f (x) = 139 + \frac{36}{x} + \frac{x ^{2}}{16}

x^{^{''}} - 6 x^{^{'}} + 25 x = 64 e^{- t}

\frac{d}{d x} (- 7 x^{3})

\frac{\partial}{\partial y} (ln (x^{2} + 1) + y^{2})

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