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Question Number 208791 by MATHEMATICSAM last updated on 23/Jun/24

$$\mathrm{If}\int \frac{dx}{x^3{(1+x^6)}^{\frac{2}{3}}}=xf\left(x\right).{(1+x^6)}^{\frac{1}{3}}+C$$$$\mathrm{where}C\mathrm{is}\mathrm{constant}\mathrm{of}\mathrm{integration}\mathrm{then}$$$$\mathrm{find}f\left(x\right).$$

Commented by mr W last updated on 23/Jun/24

$$\int ...=-\frac{{(1+x^6)}^{\frac{1}{3}}}{2x^2}+C$$$$\Rightarrow f\left(x\right)=-\frac{1}{2x^3}$$

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