<s>[INST] Solve the integral $\int \frac{dx}{\:\sqrt[4]{\left(x+2\right)^5\cdot \left(x-1\right)^3}}$ Here is a indefinite integral must be solved. Help, who knows. Although it would be like casual.
$$\int \frac{dx}{\:\sqrt[4]{\left(x+2\right)^5\cdot \left(x-1\right)^3}}$$
 [/INST] Setting $\frac{x-1}{x+2}=u$ gives you
$$dx=\frac{(x+2)^2}{3}du.$$
So,
$$\int(x+2)^{-\frac 54}(x-1)^{-\frac 34}dx=\int\frac 13u^{-\frac 34}du=\frac 43\sqrt[4]{\frac{x-1}{x+2}}+C.$$
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