A) \[\frac{{{e}^{x}}}{x+1}+C\]
B) \[\frac{{{e}^{x}}}{{{(x+1)}^{2}}}+C\]
C) \[\frac{-{{e}^{x}}}{(x+1)}+C\]
D) \[\frac{-{{e}^{x}}}{{{(x+1)}^{2}}}+C\]
Correct Answer: B
Solution :
\[I=\int{\left( \frac{x+1-2}{{{(x+1)}^{3}}} \right){{e}^{x}}dx}\] \[=\int{{{e}^{x}}\cdot \left[ \frac{1}{{{(x+1)}^{2}}}+\frac{-2}{{{(x+1)}^{3}}} \right]dx=\frac{{{e}^{x}}}{{{(x+1)}^{2}}}+C}\]
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