What is the integral of e^x3x^2 ?

The integral of e^x3x^2 is 3(x^2e^x-2(e^xx-e^x))+C

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integral of e^x3x^2

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

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

Solution steps

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

Take the constant out:

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

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

Apply Integration By Parts

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

= 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

x^{2} \frac{d ^{2} y}{d x ^{2}} - 5 x \frac{d y}{d x} + 9 y = 0

\int \frac{( x ^{2} - x + 30 )}{x ^{3} + 5 x} d x

3 x + 6 x^{3}

\frac{d}{d x} (2^{x + 1})

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

What is the integral of e^x3x^2 ?
The integral of e^x3x^2 is 3(x^2e^x-2(e^xx-e^x))+C