What is the integral of 4x^2e^x ?

The integral of 4x^2e^x is 4(x^2e^x-2(e^xx-e^x))+C

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integral of 4x^2e^x

\int 4 x^{2} e^{x} d x

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

Solution steps

\int 4 x^{2} e^{x} d x

Take the constant out:

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

= 4 \cdot \int x^{2} e^{x} d x

Apply Integration By Parts

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

= 4 (x^{2} e^{x} - \int 2 x e^{x} d x)

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

= 4 (x^{2} e^{x} - 2 (e^{x} x - e^{x}))

Add a constant to the solution

= 4 (x^{2} e^{x} - 2 (e^{x} x - e^{x})) + C

f (x) = x^{3} - 6 x^{2} + 12 x - 9

\frac{\partial}{\partial y} (- 0.2 y + 23)

\frac{\partial}{\partial x} (- 5 x y (9 - x - y))

\int \frac{1}{( 16 x ^{4} + 8 x ^{2} + 1 )} d x

\int_{0}^{2} 2 π (x + 1) (4 - 2 x) d x

What is the integral of 4x^2e^x ?
The integral of 4x^2e^x is 4(x^2e^x-2(e^xx-e^x))+C