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Question Number 124134 by bramlexs22 last updated on 01/Dec/20

$$\phi \left(x\right)=\int \left(\frac{x^3+2}{x^3}\right)\sqrt{x-\frac{1}{x^2}}dx$$

Answered by Dwaipayan Shikari last updated on 01/Dec/20

$$\int (1+\frac{2}{x^3})\left(\sqrt{x-\frac{1}{x^2}}\right)dx$$$$=\int \sqrt{t}dt=\frac{2}{3}{t}^{\frac{3}{2}}+C=\frac{2}{3}{(x-\frac{1}{x^2})}^{\frac{3}{2}}+C$$

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