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

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

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integral of arctan(x/2)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

x \to 3 lim (e (x + 1))

x \to 3 lim (\frac{3 x + 2}{x - 3})

\frac{d}{d x} (e^{a x} + 72 x)

\frac{4}{s ( s ^{2} - 4 s + 5 )}

\frac{- 5 x - 9}{2 x + 8}

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