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Let f(x)=x/(1+x^n)^(1/n) for nge2 and g(...

Let `f(x)=x/(1+x^n)^(1/n)` for `nge2` and `g(x)=ubrace(fofo…of)_("f occurs n times")(x)`. Then `intx^(n-2)g(x)dx` equals (A) `1/(n(n-1))(1+nx^n)^(1-1/n)+K` (B) `1/(n-1)(1+nx^n)^(1-1/n)+K` (C) `1/(n(n+1))(1+nx^n)^(1+1/n)+K` (D) `1/(n+1)(1+nx^n)^(1-1/n)+K`

A

`1/(n (n - 1)) (1 + nx^n)^(1 - (1//n)) + K`

B

`1/(n - 1)(1 + nx^n)^(1 - (1//n)) + K`

C

`1/(n(n - 1))(1 + nx^n)^(1 + (1//n)) + K`

D

`1/(n + 1)(1 + nx^n)^(1 + (1//n)) + K`

Text Solution

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The correct Answer is:
A
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