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

2 (x + 4)^{\frac{3}{2}}

\frac{\partial}{\partial x} (y^{2} + x^{2} - 4 x - 3)

\frac{\partial}{\partial x} (e^{x z + 2} - cos (x + y))

\frac{( e ^{x} )}{( e ^{x} + 4 ) ( x + 5 )}

csc (y) d x + sec (2) (x) d y = 0

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