What is the integral of (ye^{2y})/((1+2y)^2) ?

The integral of (ye^{2y})/((1+2y)^2) is -(e^{2y}y)/(2(1+2y))+1/4 e^{2y}+C

Popular >

integral of (ye^{2y})/((1+2y)^2)

\int \frac{y e ^{2 y}}{( 1 + 2 y ) ^{2}} d y

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

Solution steps

\int \frac{y e ^{2 y}}{( 1 + 2 y ) ^{2}} d y

Apply Integration By Parts

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

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

\int - \frac{1}{2} e^{2 y} d y = - \frac{1}{4} e^{2 y}

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

Simplify

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

Add a constant to the solution

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

\int x^{2} \frac{1}{9 - x ^{2}} d x

\int \frac{8 x}{( 5 - 2 x ) ^{5}} d x

\int (x + 2) sin (\frac{x}{2}) d x

\int (\frac{1}{x} + 5)^{2} d x

\int \frac{( x ^{4} + 9 x ^{2} + x + 2 )}{x ^{2} + 9} d x

What is the integral of (ye^{2y})/((1+2y)^2) ?
The integral of (ye^{2y})/((1+2y)^2) is -(e^{2y}y)/(2(1+2y))+1/4 e^{2y}+C