What is the integral of arctan(2y) ?

The integral of arctan(2y) is yarctan(2y)-1/4 ln|4y^2+1|+C

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integral of arctan(2y)

\int arctan (2 y) d y

y arctan (2 y) - \frac{1}{4} ln 4 y^{2} + 1 + C

Solution steps

\int arctan (2 y) d y

Apply Integration By Parts

= y arctan (2 y) - \int \frac{2 y}{4 y ^{2} + 1} d y

\int \frac{2 y}{4 y ^{2} + 1} d y = \frac{1}{4} ln 4 y^{2} + 1

= y arctan (2 y) - \frac{1}{4} ln 4 y^{2} + 1

Add a constant to the solution

= y arctan (2 y) - \frac{1}{4} ln 4 y^{2} + 1 + C

What is the integral of arctan(2y) ?
The integral of arctan(2y) is yarctan(2y)-1/4 ln|4y^2+1|+C