Question

$ \displaystyle{ \int { \ln {x} \over x^5 } \,dx } $

Answer 1

\[\int\limits \frac{ x }{ x ^{5} }dx=\int\limits x ^{-4}dx=?\]

Answer 2

\[\int\frac{\ln x}{x^5}~dx\]
Integrate by parts:
\[\begin{matrix}u=\ln x&&&dv=x^{-5}~dx\\
du=\frac{1}{x}~dx&&&v=-\frac{1}{4}x^{-4}\end{matrix}\]
\[\int\frac{\ln x}{x^5}~dx=-\frac{1}{4}x^{-4}\ln x+\frac{1}{4}\int\frac{1}{x^5}~dx\]