What is the integral of arctan(tan(x)) ?

The integral of arctan(tan(x)) is xarctan(tan(x))-(x^2)/2+C

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integral of arctan(tan(x))

\int arctan (tan (x)) d x

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

Solution steps

\int arctan (tan (x)) d x

Apply Integration By Parts

= x arctan (tan (x)) - \int x d x

\int x d x = \frac{x ^{2}}{2}

= x arctan (tan (x)) - \frac{x ^{2}}{2}

Add a constant to the solution

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

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