\(\rm \int \frac{\pi}{x^{n+1}-x} d x=\)
1
\(\rm \frac{\pi}{\mathrm{n}} \log _{e}\left|\frac{\mathrm{x}^{\mathrm{n}}-1}{\mathrm{x}^{\mathrm{n}}}\right|+C \)
2
\(\rm \log _{e}\left|\frac{x^{n}+1}{x^{n}-1}\right|+C \)
3
\( \rm \frac{\pi}{n} \log _{e}\left|\frac{x^{n}+1}{x^{n}}\right|+C \)
4
\( \rm \pi \log _{e}\left|\frac{x^{n}}{x^{n}-1}\right|+C\)