-\int_{+\infty}^1\frac{\frac{1}{t^n}\cdot\frac{1}{t^2}}{\sqrt{\frac{1}{t}\cdot\frac{1-t}{t}}}dt=\int_1^{+\infty}\frac{\frac{1}{t^{n+2}}}{\frac{\sqrt{t-1}}{t}}dt=\int_1^{+\infty}\frac{1}{t^{n+1}\sqrt{t-1}}dt