What is the integral of e^x*3x^2 ?

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

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integral of e^x*3x^2

\int e^{x} \cdot 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

\frac{d}{d x} (3 x^{4} + 2 x^{2} - 6 x + 3)

\frac{x ^{2} - 7 - 3}{x + 4}

\frac{d}{d x} (x + a x I n (b x))

y^{^{''}} + 25 y = 5 t^{2}

\frac{8}{7 x ^{9} + 3}

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