What is the integral of-8x^2e^x ?

The integral of-8x^2e^x is -8(x^2e^x-2(e^xx-e^x))+C

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integral of-8x^2e^x

\int - 8 x^{2} e^{x} d x

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

Solution steps

\int - 8 x^{2} e^{x} d x

Take the constant out:

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

= - 8 \cdot \int x^{2} e^{x} d x

Apply Integration By Parts

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

= - 8 (x^{2} e^{x} - \int 2 x e^{x} d x)

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

= - 8 (x^{2} e^{x} - 2 (e^{x} x - e^{x}))

Add a constant to the solution

= - 8 (x^{2} e^{x} - 2 (e^{x} x - e^{x})) + C

x^{\frac{3}{2}}

x \to 3 - lim (\frac{9}{( x - 3 ) ^{5}})

\int (y - 1)^{- 2} d y

\int x (x^{2} + 3)^{3} d x

\frac{d}{d x} (\frac{2 x + 1}{3 - 5 x})

What is the integral of-8x^2e^x ?
The integral of-8x^2e^x is -8(x^2e^x-2(e^xx-e^x))+C