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

The integral of arctan(tan(t)) is tarctan(tan(t))-(t^2)/2+C

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integral of arctan(tan(t))

\int arctan (tan (t)) d t

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

Solution steps

\int arctan (tan (t)) d t

Apply Integration By Parts

: t arctan (tan (t)) - \int t d t

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

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

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

Add a constant to the solution

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

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