$\begin{aligned} & \int \frac{1}{\sqrt[5]{(x-1)^4(x+3)^6}} d x=A\left(\frac{\alpha x-1}{\beta x+3}\right)^B+C \\ & I=\int \frac{1}{(x-1)^{4 / 5}(x+3)^{6 / 5}} d x \\ & I=\int \frac{1}{\left(\frac{x-1}{x+3}\right)^{4 / 5}(x+3)^2} d x \\ & \left(\frac{x-1}{x+3}\right)=t \Rightarrow \frac{4}{(x+3)^2} d x=d t \quad t^{-4 / 5+1} \\ & I=\frac{1}{4} \int \frac{1}{t^{4 / 5}} d t=\frac{1}{4} \frac{t^{1 / 5}}{1 / 5}+c \\ & I=\frac{5}{4}\left(\frac{x-1}{x+3}\right)^{1 / 5}+C \\ & A=\frac{5}{4} \quad \alpha=\beta=1 \quad B=\frac{1}{5} \\ & \alpha+\beta+20 A B=2+20 \times \frac{5}{4} \times \frac{1}{5}=7\end{aligned}$