∫(3−x21−2x+x2) ex dx=exf(x)+c⇒f(x)=

∫ex[3−x2(1−x)2]dx =∫ex[2+1−x2(1−x)2]dx =∫ex[2(1−x)2+1+x1−x]dx =ex|1+x1−x|+c

∫(3−x21−2x+x2) ex dx=exf(x)+c⇒f(x)=

∫ex[3−x2(1−x)2]dx =∫ex[2+1−x2(1−x)2]dx =∫ex[2(1−x)2+1+x1−x]dx =ex|1+x1−x|+c

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$\int (\frac{3 - x^{2}}{1 - 2 x + x^{2}}) e^{x} d x = e^{x} f (x) + c \Rightarrow f (x) =$

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$\frac{1 + x}{1 - x}$

$\frac{1 - x}{1 + x}$

$\frac{1 + x}{x - 1}$

$\frac{x - 1}{x + 1}$

answer is A.

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Detailed Solution

$\int e^{x} [\frac{3 - x^{2}}{{(1 - x)}^{2}}] d x$

$= \int e^{x} [\frac{2 + 1 - x^{2}}{{(1 - x)}^{2}}] d x$

$= \int e^{x} [\frac{2}{{(1 - x)}^{2}} + \frac{1 + x}{1 - x}] d x$

$= e^{x} | \frac{1 + x}{1 - x} | + c$

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∫(3−x21−2x+x2) ex dx=exf(x)+c⇒f(x)=

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$\int (\frac{3 - x^{2}}{1 - 2 x + x^{2}}) e^{x} d x = e^{x} f (x) + c \Rightarrow f (x) =$