If ∫1×1−x3dx=a9log⁡1−x2−11−x2+1+b, then a is equal to

If 1x1x3dx=a9log1x211x2+1+b, then a is equal to

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    Solution:

    Putting 1x3=y2,3x2dx=2ydy, we get

    I=1x1x3dx=2311y2dy=231y21dy

     I=13logy1y+1+C=13log1x311x3+1+C

    Hence, a=3

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