What is the integral of arctan(v) ?

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

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integral of arctan(v)

\int arctan (v) d v

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

Solution steps

\int arctan (v) d v

Apply Integration By Parts

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

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

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

Add a constant to the solution

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

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