What is the integral of-3x^2e^x ?

The integral of-3x^2e^x is -3(x^2e^x-2(e^xx-e^x))+C

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integral of-3x^2e^x

\int - 3 x^{2} e^{x} d x

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

Solution steps

\int - 3 x^{2} e^{x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 3 \cdot \int x^{2} e^{x} d x

Apply Integration By Parts

= - 3 (x^{2} e^{x} - \int 2 x e^{x} d x)

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

= - 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x}))

Add a constant to the solution

= - 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x})) + C

\frac{d}{d x} (7 (3 x + \frac{x ^{\frac{1}{3}}}{3}))

\frac{\partial}{\partial x} (x + 3 lo g_{10} (x) - y^{2})

\int \frac{18}{x 1 + 2 x} d x

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

y^{^{''}} - 5 y^{^{'}} + 4 y = 0

What is the integral of-3x^2e^x ?
The integral of-3x^2e^x is -3(x^2e^x-2(e^xx-e^x))+C