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Question Number 184112 by cortano1 last updated on 03/Jan/23

$$\int \frac{dx}{{(x-1)}^{5/6}{(x+2)}^{7/6}}=?$$

Commented by sahalu last updated on 03/Jan/23

$$\int \frac{dx}{{(x-1)}^{5/6}{(x+2)}^{7/6}}=?\begin{array}{c}\int \\ \end{array}\}$$

Answered by Frix last updated on 03/Jan/23

$$\int \frac{dx}{{(x-1)}^{\frac{5}{6}}{(x+2)}^{\frac{7}{6}}}\stackrel{[t={\left(\frac{x-1}{x+2}\right)}^{\frac{1}{6}}]}{=}$$$$=2\int dt=2t=2{\left(\frac{x-1}{x+2}\right)}^{\frac{1}{6}}+C$$

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