What is the integral of (x^2)/(e^{3x)} ?

The integral of (x^2)/(e^{3x)} is -1/3 e^{-3x}x^2+2/27 (-3e^{-3x}x-e^{-3x})+C

integral of (x^2)/(e^{3x)}

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

- \frac{1}{3} e^{- 3 x} x^{2} + \frac{2}{27} (- 3 e^{- 3 x} x - e^{- 3 x}) + C

Solution steps

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

Apply Integration By Parts

= - \frac{1}{3} e^{- 3 x} x^{2} - \int - \frac{2}{3} e^{- 3 x} x d x

\int - \frac{2}{3} e^{- 3 x} x d x = - \frac{2}{27} (- 3 e^{- 3 x} x - e^{- 3 x})

= - \frac{1}{3} e^{- 3 x} x^{2} - (- \frac{2}{27} (- 3 e^{- 3 x} x - e^{- 3 x}))

Simplify

= - \frac{1}{3} e^{- 3 x} x^{2} + \frac{2}{27} (- 3 e^{- 3 x} x - e^{- 3 x})

Add a constant to the solution

= - \frac{1}{3} e^{- 3 x} x^{2} + \frac{2}{27} (- 3 e^{- 3 x} x - e^{- 3 x}) + C

a re a x = 7 y^{2}, x = 4 + 6 y^{2}

\frac{d}{d x} (\frac{- 2 ln ( x ) + 1}{x ^{3}})

l a pl a ce t r an s f or m 3 x

\int \frac{x - 9}{x ^{2} + 3 x - 10} d x

\int_{0}^{1} \frac{3}{2} x d x

What is the integral of (x^2)/(e^{3x)} ?
The integral of (x^2)/(e^{3x)} is -1/3 e^{-3x}x^2+2/27 (-3e^{-3x}x-e^{-3x})+C