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

The integral of x^2e^x is x^2e^x-2(e^xx-e^x)+C

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integral of x^2e^x

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

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

Solution steps

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

Apply Integration By Parts

: x^{2} e^{x} - \int 2 x e^{x} d x

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

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

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

Add a constant to the solution

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

\int_{2}^{10} - 4 d x

\frac{1}{s ^{2} + π ^{2}}

x^{2}, - x + 6

(6 + x) y^{^{'}} = 3 y

2 x^{2} - 3 x