∫x2(ax+b)−2dx is equal to

x2(ax+b)2dx is equal to

  1. A

    2a2x2balog(ax+b)+C

  2. B

    2a2x2balog(ax+b)b2a3(ax+b)+C

  3. C

    2a2x2+balog(ax+b)+b2a3(ax+b)+C

  4. D

    2a2x2+balog(ax+b)b2a3(ax+b)+C

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    Solution:

    I=x2(ax+b)2dx

    put  ax+b=tdx=1adt and x=tba

     I=1a3(tb)2t2dt=1a31+b2t22btdt=1a3tb2t2blogt+C

                                         =1a3ax+bb2ax+b2blog(ax+b)+C=2a2x2balog(ax+b)b2a3(ax+b)+C

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