What is the integral of (x^2)/(e^{7x)} ?

The integral of (x^2)/(e^{7x)} is -1/7 e^{-7x}x^2+2/343 (-7e^{-7x}x-e^{-7x})+C

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integral of (x^2)/(e^{7x)}

\int \frac{x ^{2}}{e ^{7 x}} d x

- \frac{1}{7} e^{- 7 x} x^{2} + \frac{2}{343} (- 7 e^{- 7 x} x - e^{- 7 x}) + C

Solution steps

\int \frac{x ^{2}}{e ^{7 x}} d x

Apply Integration By Parts

: - \frac{1}{7} e^{- 7 x} x^{2} - \int - \frac{2}{7} e^{- 7 x} x d x

= - \frac{1}{7} e^{- 7 x} x^{2} - \int - \frac{2}{7} e^{- 7 x} x d x

\int - \frac{2}{7} e^{- 7 x} x d x = - \frac{2}{343} (- 7 e^{- 7 x} x - e^{- 7 x})

= - \frac{1}{7} e^{- 7 x} x^{2} - (- \frac{2}{343} (- 7 e^{- 7 x} x - e^{- 7 x}))

Simplify

= - \frac{1}{7} e^{- 7 x} x^{2} + \frac{2}{343} (- 7 e^{- 7 x} x - e^{- 7 x})

Add a constant to the solution

= - \frac{1}{7} e^{- 7 x} x^{2} + \frac{2}{343} (- 7 e^{- 7 x} x - e^{- 7 x}) + C

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What is the integral of (x^2)/(e^{7x)} ?
The integral of (x^2)/(e^{7x)} is -1/7 e^{-7x}x^2+2/343 (-7e^{-7x}x-e^{-7x})+C