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

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

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integral of x^2(e^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

x \to - 2 lim (\frac{2 x + 2}{x - 1})

\frac{6 x}{1 - tan ( x )}

\int \frac{x - 3}{x + 1} d x

y^{^{''}} - y^{^{'}} - 6 y = 0, y (0) = 1, y^{^{'}} (0) = 0

\int \frac{9}{x ( x + 3 )} d x

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