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JEE Main & Advanced Sample Paper JEE Main Sample Paper-18

  • question_answer
    If\[\int{\frac{(2x+3)dx}{x(x+1)\,(x+2)\,(x+3)+1}}=C-\frac{1}{f(x)}\] . Where \[f(x)\] is of the form of\[a{{x}^{2}}+bx+c\]then the value of\[f(1)\]is

    A)  4                                            

    B)  5

    C)  6                                            

    D)  none

    Correct Answer: B

    Solution :

     \[I=\int{\frac{2x+3}{({{x}^{2}}+3x)({{x}^{2}}+3x+2)+1}}dx\] Put \[{{x}^{2}}+3x=t\] \[\Rightarrow \]               \[(2x+3)dx=dt\] \[\Rightarrow \]               \[I=\int{\frac{dt}{t(t+2)+1}}\] \[=\int{\frac{dt}{{{(t+1)}^{2}}}}\] \[=C-\frac{1}{t+1}\] \[=C-\frac{1}{{{x}^{2}}+3x+1}\] \[\therefore \] \[f(1)=5\]


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