What is the integral of 8arctan(2y) ?

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

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integral of 8arctan(2y)

\int 8 arctan (2 y) d y

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

Solution steps

\int 8 arctan (2 y) d y

Take the constant out:

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

= 8 \cdot \int arctan (2 y) d y

Apply Integration By Parts

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

= 8 (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

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

Add a constant to the solution

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

t^{3} e^{7 t}

\frac{\partial}{\partial y} (e^{x^{2}} - y)

\int sin (120 π x) d x

f (x) = 4 x^{2} - x^{3}, (1, 3)

y = - x^{2} - 2 x + 2, (- 3, - 1)

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