What is the integral of arctan(y) ?

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

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integral of arctan(y)

\int arctan (y) d y

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

Solution steps

\int arctan (y) d y

Apply Integration By Parts

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

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

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

Add a constant to the solution

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

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