What is the integral of (x^2-2x+5)e^{-x} ?

The integral of (x^2-2x+5)e^{-x} is -e^{-x}x^2-5e^{-x}+C

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integral of (x^2-2x+5)e^{-x}

\int (x^{2} - 2 x + 5) e^{- x} d x

- e^{- x} x^{2} - 5 e^{- x} + C

Solution steps

\int (x^{2} - 2 x + 5) e^{- x} d x

Apply Integration By Parts

: - e^{- x} (x^{2} - 2 x + 5) - \int - e^{- x} (2 x - 2) d x

= - e^{- x} (x^{2} - 2 x + 5) - \int - e^{- x} (2 x - 2) d x

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

= - e^{- x} (x^{2} - 2 x + 5) - 2 e^{- x} x

Simplify

- e^{- x} (x^{2} - 2 x + 5) - 2 e^{- x} x : - e^{- x} x^{2} - 5 e^{- x}

= - e^{- x} x^{2} - 5 e^{- x}

Add a constant to the solution

= - e^{- x} x^{2} - 5 e^{- x} + C

x \to - 2 lim (7 x^{2} + 8)

cos (- 3 x)

sin (t) - sin (t) cos (t) - 5 t

f (t) = - \frac{50}{t ^{3}} + \frac{5}{t ^{2}}

\int e tan (x) d x

What is the integral of (x^2-2x+5)e^{-x} ?
The integral of (x^2-2x+5)e^{-x} is -e^{-x}x^2-5e^{-x}+C