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$If \int \frac{d x}{x^{2} {(x^{n} + 1)}^{(n - 1) / n}} = - [f (x)]^{1 / n} + c, then f (x) is$

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Correct option is B

We have ∫dxx2xn+1(n−1)/n=∫dxx2xn−11+1xn(n−1)/n =∫dxxn+11+x−n(n−1)/n Put 1+x−n=t∴−nx−n−1dx=dt or dxxn+1=−dtn∴∫dxx2xn+1(n−1)/n=−1n∫dtt(n−1)/n=−1n∫1-nn t =−1nt1-nn+11-nn+1+C =−t1/n+C=−1+x−n1/n+C

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If ∫dxx2xn+1(n−1)/n=−[f(x)]1/n+c, then f(x) is

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$If \int \frac{d x}{x^{2} {(x^{n} + 1)}^{(n - 1) / n}} = - [f (x)]^{1 / n} + c, then f (x) is$