Can someone explain,why i can`t integrate this? $$\int\frac{\ln^5 x}xdx=\int\ln^5 x\ d(\ln x)$$
I`m really sorry for stupid question.
2026-04-03 19:55:31.1775246131
How to integrate $\int\frac{\ln^5 x}xdx$?
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Hint. You may observe that $$ \int f'(x)(f(x))^ndx=\frac1{n+1} (f(x))^{n+1}+C,\quad n \neq-1, $$ then rewrite your integral as $$ \int\frac{\ln^5 x}xdx=\int(\ln x)'(\ln x)^5\: dx. $$ Hoping you can take it from here.