$\int e^{x} (x^{2} - 5 x + 8)$ dx $= e^{x} f (x) + c$ then $f (x)$

x^{2} - 5 x + 12

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x^{2} + 7 x + 15

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x^{2} - 7 x - 15

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x^{2} - 7 x + 15

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Solution

The correct option is C $x^{2} - 7 x + 15$
$\int e^{x} (x^{2} - 5 x + 8) d x$
$= \int e^{x} x^{2} d x - 5 \int e^{x} . x d x + 8 \int e^{x} d x$
$= x^{2} e^{x} = 2 \int x e^{x} d x - 5 \int e^{x} x + 8 \int e^{x} d x$
$x^{2} e^{x} - 7 [x e^{x} - e^{x}] + 8 e^{x}$
$= x^{2} e^{x} - 7 x e^{x} + 15 e^{x}$
$= e^{n} [x^{2} - 7 x + 15] + c$
$s o, f (x) - x^{2} - 7 x + 15$

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