What is the integral of 2arctan(4y) ?

The integral of 2arctan(4y) is 2(yarctan(4y)-1/8 ln|16y^2+1|)+C

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integral of 2arctan(4y)

\int 2 arctan (4 y) d y

2 (y arctan (4 y) - \frac{1}{8} ln 16 y^{2} + 1) + C

Solution steps

\int 2 arctan (4 y) d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int arctan (4 y) d y

Apply Integration By Parts

: y arctan (4 y) - \int \frac{4 y}{16 y ^{2} + 1} d y

= 2 (y arctan (4 y) - \int \frac{4 y}{16 y ^{2} + 1} d y)

\int \frac{4 y}{16 y ^{2} + 1} d y = \frac{1}{8} ln 16 y^{2} + 1

= 2 (y arctan (4 y) - \frac{1}{8} ln 16 y^{2} + 1)

Add a constant to the solution

= 2 (y arctan (4 y) - \frac{1}{8} ln 16 y^{2} + 1) + C

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What is the integral of 2arctan(4y) ?
The integral of 2arctan(4y) is 2(yarctan(4y)-1/8 ln|16y^2+1|)+C