What is the integral of 9x^2e^x ?

The integral of 9x^2e^x is 9(x^2e^x-2(e^xx-e^x))+C

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integral of 9x^2e^x

\int 9 x^{2} e^{x} d x

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

Solution steps

\int 9 x^{2} e^{x} d x

Take the constant out:

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

= 9 \cdot \int x^{2} e^{x} d x

Apply Integration By Parts

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

= 9 (x^{2} e^{x} - \int 2 x e^{x} d x)

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

= 9 (x^{2} e^{x} - 2 (e^{x} x - e^{x}))

Add a constant to the solution

= 9 (x^{2} e^{x} - 2 (e^{x} x - e^{x})) + C

x^{2} = e^{x - y}

\frac{d}{d x} (cos (x^{7}))

\frac{d}{d x} (sin^{3} (x^{4}))

2^{x + 2}

\int \frac{1}{4 x + 8} d x

What is the integral of 9x^2e^x ?
The integral of 9x^2e^x is 9(x^2e^x-2(e^xx-e^x))+C