x-3-2-x-3-x-1-x-2-

Question Number 89226 by cindiaulia last updated on 16/Apr/20

\int (\frac{x^{3} + 2}{x^{3}}) \sqrt{x - \frac{1}{x^{2}}}

Commented by jagoll last updated on 16/Apr/20

\int (1 + \frac{2}{x^{3}}) \sqrt{x - \frac{1}{x^{2}}} d x

u = x - \frac{1}{x^{2}} \Rightarrow d u = 1 + \frac{2}{x^{3}}

\int u^{\frac{1}{2}} d u = \frac{2}{3} u^{\frac{3}{2}} + c

= \frac{2}{3} {(x - \frac{1}{x^{2}})}^{\frac{3}{2}} + c

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