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

= 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

\int \frac{2}{1 - x} d x

y^{^{'}} - y = x + 1

\frac{2 s}{s ^{2} - 8 s + 6}

\frac{d}{d x} (x^{\frac{l n ( 2 )}{( 1 + l n ( x ) )}})

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