# What is f(x) = int x^2e^(x-1)-x^3e^-x dx if f(2) = 7 ?

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May 25, 2018

#### Answer:

your integral is given by
${x}^{3} {e}^{-} x + {x}^{2} {e}^{x - 1} + 3 {x}^{2} {e}^{- x} - 2 x {e}^{x - 1} + 6 {e}^{- x} x + 2 {e}^{x - 1} + 6 {e}^{- x} + C$

#### Explanation:

I have got this after several times integrating by parts.
We get $C$ by the following equation
$38 {e}^{- 2} + 2 e + C = 7$

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