The value of ∫ex1+nxn−1−x2n1−xn1−x2ndx is equal to 

The value of ex1+nxn1x2n1xn1x2ndx is equal to 

  1. A

    ex1x2+C

  2. B

    ex1+x2n1+x2n+C

  3. C

    ex1xn1x2n+C

  4. D

    ex1x2n1xn+C

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    Solution:

    Let f(x)=1x2n1xn

    f(x)=1xn121+xn.nxn-11+xn121-xn.-nxn-11xnf'(x)=1xn.nxn1+1+xn.nxn-121xn1x2nf'(x)=nxn11xn1x2n

     I=ex1+nxn1x2n1xn1x2ndx=ex1x2n1xn+nxn11xn1x2ndx   

             =ex(f(x)+f'(x)dx=exf(x)+c

            =ex1x2n1xn+c

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