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If $I = \int \frac{d x}{x^{3} {(1 + x^{6})}^{2 / 3}} = f (x) {(1 + x^{- 6})}^{1 / 3} + C,$ where $C$ is a constant of integration, then $f (x)$ is equal to:

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Correct option is D

I=∫dxx31+x62/3=∫dxx3⋅x62/3x−6+12/3 =∫x−7x−6+12/3dx =−16⋅3x−6+11/3+C [Put x-6+1=t]∴ f(x)=−1/2

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If I=∫dxx31+x62/3=f(x)1+x−61/3+C, where C is a constant of integration, then f(x) is equal to:

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If $I = \int \frac{d x}{x^{3} {(1 + x^{6})}^{2 / 3}} = f (x) {(1 + x^{- 6})}^{1 / 3} + C,$ where $C$ is a constant of integration, then $f (x)$ is equal to: