What is the integral of y^2e^{3y} ?

The integral of y^2e^{3y} is 1/3 e^{3y}y^2-2/27 (3e^{3y}y-e^{3y})+C

Popular >

integral of y^2e^{3y}

\int y^{2} e^{3 y} d y

\frac{1}{3} e^{3 y} y^{2} - \frac{2}{27} (3 e^{3 y} y - e^{3 y}) + C

Solution steps

\int y^{2} e^{3 y} d y

Apply Integration By Parts

: \frac{1}{3} e^{3 y} y^{2} - \int \frac{2}{3} e^{3 y} y d y

= \frac{1}{3} e^{3 y} y^{2} - \int \frac{2}{3} e^{3 y} y d y

\int \frac{2}{3} e^{3 y} y d y = \frac{2}{27} (3 e^{3 y} y - e^{3 y})

= \frac{1}{3} e^{3 y} y^{2} - \frac{2}{27} (3 e^{3 y} y - e^{3 y})

Add a constant to the solution

= \frac{1}{3} e^{3 y} y^{2} - \frac{2}{27} (3 e^{3 y} y - e^{3 y}) + C

n = 0 \sum \infty \frac{1}{n + 7}

\int_{0}^{9} \frac{8}{( x - 1 ) ^{\frac{1}{3}}} d x

\frac{\partial}{\partial x} (9 x \cdot cos (x) \cdot cos (y))

\frac{d}{d x} (- 2 cos (x) - x)

\int sin (a - x) d x

What is the integral of y^2e^{3y} ?
The integral of y^2e^{3y} is 1/3 e^{3y}y^2-2/27 (3e^{3y}y-e^{3y})+C