What is the integral of y^2e^y ?

The integral of y^2e^y is y^2e^y-2(e^yy-e^y)+C

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integral of y^2e^y

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

y^{2} e^{y} - 2 (e^{y} y - e^{y}) + C

Solution steps

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

Apply Integration By Parts

= y^{2} e^{y} - \int 2 y e^{y} d y

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

= y^{2} e^{y} - 2 (e^{y} y - e^{y})

Add a constant to the solution

= y^{2} e^{y} - 2 (e^{y} y - e^{y}) + C

s l o p e (- 6, 6), (4, - 7)

3 y^{^{''}} = 2 y^{^{'}}

\int cos (x^{2}) d x

\int \frac{x ^{2}}{x ^{2} + 8} d x

\frac{d}{d x} (6 sin^{2} (2 x) cos (2 x) + 2 x)