A) \[-\frac{1}{(x+1)}+c\]
B) \[\frac{1}{5}\log \,\,(x+1)+c\]
C) \[\log \,(x+1)+c\]
D) \[{{\tan }^{-1}}x+c\]
Correct Answer: A
Solution :
Let \[I=\int{\frac{({{x}^{3}}+3{{x}^{2}}+3x+1)}{{{(x+1)}^{5}}}dx}\] \[=\int{\frac{{{(x+1)}^{3}}}{{{(x+1)}^{5}}}}dx=\int{\frac{1}{{{(x+1)}^{2}}}}dx\] \[=-\frac{1}{(x+1)}+c\]
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