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If f(x)=(x)/((1+x^(n))^(1//n)) "for n" g...

If `f(x)=(x)/((1+x^(n))^(1//n)) "for n" ge 2 and g(x) = underset("f occurs n times")ubrace(("fofo....of"))(x). "Then",intx^(n-2)g(x) dx` equal

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Given, `f(x)=(x)/((1+x^(n))^(1//n))"for n" ge 2`
`therefore" "ff(x)=(f(x))/([1+f(x)^(n)]^(1//n))=(x)/(1+2x^(n))^(1//n) and fff(x) = (x)/((1+3x^(n))^(1//n))`
`therefore" "g(x)=underset("n times")ubrace("fofo....of")(x)=(x)/((1+nx^(n))^(1//n))`
`"Let"" "I=int x^(n-1)g(x)dx = int(x^(n-1)dx)/((1+nx^(n))^(1//n))`
`" "=(1)/(n^(2))int(n^(2)x^(n-1)dx)/((1+nx^(n))^(1//n))=(1)/(n^(2))int((d)/(dx)(1+nx^(n)))/((1+nx^(n))^(1//n))dx`
`" "I=(1)/(n(n-1))(1+nx^(n))^(1-(1)/(n))+c`
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