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

y = x^{3} + 1, (0, 2)

x \to \infty + lim (x^{2} x)

\frac{\partial}{\partial y} (\frac{e ^{x}}{1 + y})

\int \frac{tan ^{5} ( x )}{sec ^{8} ( x )} d x

\int_{0}^{4} π (16 x^{2} - x^{4}) d x

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