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JEE Main & Advanced JEE Main Online Paper (Held on 9 April 2013)

  • question_answer
                    If \[\int{\frac{dx}{x+{{x}^{7}}}=P(x)}\]then,\[\int{\frac{{{x}^{6}}}{x+{{x}^{7}}}=dx}\] is equal to :                   JEE Main Online Paper (Held On 09 April 2013)

    A)                 \[ln\left| x \right|-p(x)+c\]                

    B)                 \[ln\left| x \right|+p(x)+c\]                

    C)                 \[x-p(x)+c\]                

    D)                 \[x+p(x)+c\]­­                

    Correct Answer: A

    Solution :

                    Let \[l=\int_{{}}^{{}}{\frac{{{x}^{6}}}{x+{{x}^{7}}}dx=\int_{{}}^{{}}{\frac{{{x}^{6}}}{x(1+{{x}^{6}})}dx}}\]                 \[=\int_{{}}^{{}}{\frac{(1+{{x}^{6}})-1}{x(1+{{x}^{6}})}}\] \[\Rightarrow \]               \[l=\int_{{}}^{{}}{\frac{dx}{x}-\int_{{}}^{{}}{\frac{dx}{x+{{x}^{7}}}=\log \,|x|-P(x)+C}}\]                


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