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JEE Main & Advanced Mathematics Indefinite Integrals Question Bank Fundamental Integration

  • question_answer
    The value of \[\int{\frac{1}{{{(x-5)}^{2}}}\,\,dx}\] is [Karnataka CET 2001; Pb. CET 2002]

    A)            \[\frac{1}{x-5}+c\]

    B)            \[-\frac{1}{x-5}+c\]

    C)            \[\frac{2}{{{\left( x-5 \right)}^{3}}}+c\]

    D)  \[-2{{\left( x-5 \right)}^{3}}+c\]

    Correct Answer: B

    Solution :

               \[I=\int{\frac{1}{{{(x-5)}^{2}}}dx}\]\[=\frac{{{(x-5)}^{-2+1}}}{-2+1}+c=\frac{{{(x-5)}^{-1}}}{-1}+c\]                       \[=-\frac{1}{(x-5)}+c\].


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