The correct option is B e^x( x + 1)^2 + c =∫e^x(x 1)x+1^3dx =∫e^x(x+1)(x+1)^3dx 2∫e^x(x+1)dx =∫e^xdx(x+1)^2 2∫e^x(x+1)^3dx Applying integra ...

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Integration by Substitution

Solve ∫exx-...

Question

Solve $\int \frac{e^{x} (x - 1)}{(x + 1)^{3}} d x$

\frac{- e^{x}}{{(x + 1)}^{2}} + c

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\frac{e^{x}}{{(x + 1)}^{2}} + c

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\frac{e^{x}}{{(x + 1)}^{3}} + c

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{- e^{x}}{{(x + 1)}^{3}} + c

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Solution

The correct option is B $\frac{e^{x}}{{(x + 1)}^{2}} + c$
$= \int {\frac{e^{x} (x - 1)}{x + 1}}^{3} d x$
$= \int \frac{e^{x} (x + 1)}{(x + 1)^{3}} d x - 2 \int \frac{e^{x}}{(x + 1)} d x$
$= \int \frac{e^{x} d x}{(x + 1)^{2}} - 2 \int \frac{e^{x}}{(x + 1)^{3}} d x$
Applying integration by parts on firsttem
$\frac{e^{x}}{(x + 1)^{2}} +^{2} \int \frac{e^{x}}{(x + 1)^{3}} - \int \frac{e^{x}}{(x + 1)^{3}} + c$
$\frac{e^{x}}{(x + 1)^{2}} + c .$
$B$ is correct

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