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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2008

  • question_answer
        \[\int{\frac{({{x}^{3}}+3{{x}^{2}}+3x+1)}{{{(x+1)}^{5}}}}dx\]is equal to

    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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