The correct option is B e^x ( x 1/x+1 )+C ∫ e^x #160; ( ( x^2 1 )(x+1)^2+1/(x+1)^2 #160; )dx ∫ e^x ( x 1x+1+1(x+1)^2 )dx=e^x ( x 1x+1 ...

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Special Integrals - 1

∫ ex X2+1X+...

Question

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

\frac{e^{x}}{x + 1} + C

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\frac{- e^{x}}{x - 1} + C

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

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

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Solution

The correct option is B $e^{x} (\frac{x - 1}{x + 1}) + C$
$\int e^{x}$ $(\frac{(x^{2} - 1)}{(x + 1)^{2}} + \frac{1}{(x + 1)^{2}}) d x$
$\int e^{x} (\frac{x - 1}{x + 1} + \frac{1}{(x + 1)^{2}}) d x = e^{x} (\frac{x - 1}{x + 1}) + C$

$e^{x} (\frac{x - 1}{x + 1}) + C$

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