What is the integral of x^2e^{x/6} ?

The integral of x^2e^{x/6} is 6e^{x/6}x^2-12(6e^{x/6}x-36e^{x/6})+C

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integral of x^2e^{x/6}

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

6 e^{\frac{x}{6}} x^{2} - 12 (6 e^{\frac{x}{6}} x - 36 e^{\frac{x}{6}}) + C

Solution steps

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

Apply Integration By Parts

: 6 e^{\frac{x}{6}} x^{2} - \int 12 e^{\frac{x}{6}} x d x

= 6 e^{\frac{x}{6}} x^{2} - \int 12 e^{\frac{x}{6}} x d x

\int 12 e^{\frac{x}{6}} x d x = 12 (6 e^{\frac{x}{6}} x - 36 e^{\frac{x}{6}})

= 6 e^{\frac{x}{6}} x^{2} - 12 (6 e^{\frac{x}{6}} x - 36 e^{\frac{x}{6}})

Add a constant to the solution

= 6 e^{\frac{x}{6}} x^{2} - 12 (6 e^{\frac{x}{6}} x - 36 e^{\frac{x}{6}}) + C

\frac{\partial}{\partial x} (- x yz + 54)

3 e^{x^{2}}

f (x) = \frac{1}{3} x^{3} - 14 x^{2} + 6 x + 1

\frac{d}{d x} (- x + \frac{8}{x} + 1)

y^{^{''}} + 10 y^{^{'}} + 24 y = 0

What is the integral of x^2e^{x/6} ?
The integral of x^2e^{x/6} is 6e^{x/6}x^2-12(6e^{x/6}x-36e^{x/6})+C