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

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

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integral of 3x^2e^x

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

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

Solution steps

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

Take the constant out:

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

= 3 \cdot \int x^{2} e^{x} 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{\partial}{\partial x} (- 2 y csc^{3} (x))

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

\int \frac{3}{2} x e^{- 6 x} d x

6 + \frac{1}{5} sin (6 π t)

x \to 0 lim ((1 + 3 x)^{\frac{2}{x}})

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