Find the integral ∫lnxxn dx\int \frac{\ln x}{x^n} \, dx∫xnlnxdx (n≠1n \neq 1n=1).
x1−n1−nlnx−x1−n(1−n)2+C\frac{x^{1-n}}{1-n} \ln x - \frac{x^{1-n}}{(1-n)^2} + C1−nx1−nlnx−(1−n)2x1−n+C
x1−n1−nlnx+x1−n(1−n)2+C\frac{x^{1-n}}{1-n} \ln x + \frac{x^{1-n}}{(1-n)^2} + C1−nx1−nlnx+(1−n)2x1−n+C
x1−n1−n(lnx−1)+C\frac{x^{1-n}}{1-n} (\ln x - 1) + C1−nx1−n(lnx−1)+C
xn−1n−1lnx+C\frac{x^{n-1}}{n-1} \ln x + Cn−1xn−1lnx+C