What is the integral of arctan(2/x) ?

The integral of arctan(2/x) is xarctan(2/x)+ln|4+x^2|+C

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integral of arctan(2/x)

\int arctan (\frac{2}{x}) d x

x arctan (\frac{2}{x}) + ln 4 + x^{2} + C

Solution steps

\int arctan (\frac{2}{x}) d x

Apply Integration By Parts

: x arctan (\frac{2}{x}) - \int - \frac{2 x}{4 + x ^{2}} d x

= x arctan (\frac{2}{x}) - \int - \frac{2 x}{4 + x ^{2}} d x

\int - \frac{2 x}{4 + x ^{2}} d x = - ln 4 + x^{2}

= x arctan (\frac{2}{x}) - (- ln 4 + x^{2})

Simplify

= x arctan (\frac{2}{x}) + ln 4 + x^{2}

Add a constant to the solution

= x arctan (\frac{2}{x}) + ln 4 + x^{2} + C

1 - u

y^{^{'}} = 4 - 0.75 y

n = 2 \sum \infty \frac{8}{n ^{2} - 1}

\frac{1}{x ^{2}} - x, x = 2, x = 3

\frac{\partial}{\partial u} (cos (u))

What is the integral of arctan(2/x) ?
The integral of arctan(2/x) is xarctan(2/x)+ln|4+x^2|+C