What is the integral of e^{-sx}*x^2 ?

The integral of e^{-sx}*x^2 is -e^{-sx} 1/s x^2+2/(s^3)(-se^{-sx}x-e^{-sx})+C

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integral of e^{-sx}*x^2

\int e^{- s x} \cdot x^{2} d x

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

Solution steps

\int e^{- s x} x^{2} d x

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

- x^{2} + 9 x + 3, at x = 5

y = x^{2}, y = x, y = 0

n = 2 \sum \infty e^{3 - 4 n}

f (x) = (2 x - 8) 4 (x^{2} + x + 1) 5

\frac{s + 2}{s ^{2} - s - 12}

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