What is the integral of yarctan(2y) ?

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

Popular >

integral of yarctan(2y)

\int y arctan (2 y) d y

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

Solution steps

\int y arctan (2 y) d y

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

6 y^{^{''}} + y = 0

y^{^{'}} - \frac{6}{x} y = \frac{y ^{3}}{x ^{9}}

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

\frac{\partial}{\partial x} (c)

x^{2} y^{^{''}} - x y^{^{'}} + y - ln (x) = 0

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