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

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

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integral of arctan(cot(x))

\int arctan (cot (x)) d x

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

Solution steps

\int arctan (cot (x)) d x

Apply Integration By Parts

: x arctan (cot (x)) - \int - x d x

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

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

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

Simplify

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

Add a constant to the solution

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

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