What is the integral of arctan(z) ?

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

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integral of arctan(z)

\int arctan (z) d z

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

Solution steps

\int arctan (z) d z

Apply Integration By Parts

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

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

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

Add a constant to the solution

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

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