What is the integral of arctan((2x)/(1-x^2)) ?

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

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integral of arctan((2x)/(1-x^2))

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

Add a constant to the solution

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

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