Let f(x) = x (1 + x^n)^ 1/n for n ≥ 2 and g(x) = (f f f) _ f occurs n times (x). Then x^ n-2 g(x) ,dx equals

JEE Advanced 2007 Mathematics question

Let for n ≥ 2 and . Then equals

Answer: (A)

with , so ; by induction the n-fold composition is . Then $ =

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Question ID VK-037521