If `int(dx)/(x^2(x^n+1)^((n-1)/n))=-(f(x))^(1/n)+C` then `f(x)` is (A) `1+x^n` (B) `1+x^-n` (C) `x^n+x^-n` (D) `x^n-x^-n`A. `(1+x^(n))`B. `1+x^(-n) `C. `x^(n)+x^(-n) `D. non of these

If `int(dx)/(x^2(x^n+1)^((n-1)/n))=-(f(x))^(1/n)+C` then `f(x)` is (A)

1.	If `int(dx)/(x^2(x^n+1)^((n-1)/n))=-(f(x))^(1/n)+C` then `f(x)` is (A) `1+x^n` (B) `1+x^-n` (C) `x^n+x^-n` (D) `x^n-x^-n`A. `(1+x^(n))`B. `1+x^(-n) `C. `x^(n)+x^(-n) `D. non of these
Answer» Correct Answer - B `"We have " int(dx)/(x^(2)(x^(n)+1)^((n-1)//n))=int(dx)/(x^(2)x^(n-1)(1+(1)/(x^(n)))^((n-1)//n))` `=int(dx)/(x^(n+1)(1+x^(-n))^((n-1)//n))` `"Put " 1+x^(-n)=t` ` :. -nx^(-n-1)dx=dt " or " (dx)/(x^(n+1))=-(dt)/(n)` ` :. int(dx)/(x^(2)(x^(n)+1)^((n-1)//n))=-(1)/(n)int(dt)/(t^((n-1)//n)) ` `=-(1)/(n)int t^(((1)/(n)-1))dt ` `=-(1)/(n)(t^((1)/(n)-1+1))/((1)/(n)-1+1)+C` `=-t^(1//n)+C` `=-(1+x^(-n))^(1//n)+C`

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