What is the integral of arctan(u) ?

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

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integral of arctan(u)

\int arctan (u) d u

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

Solution steps

\int arctan (u) d u

Apply Integration By Parts

: u arctan (u) - \int \frac{u}{u ^{2} + 1} d u

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

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

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

Add a constant to the solution

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

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2 x^{3} - 5

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\frac{d}{d t} (3 t)

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