Question Number 96672 by 175 last updated on 03/Jun/20
$${Evaluate}\:: \\ $$$$\int\:\frac{{log}_{{x}} {a}}{{x}}\:{dx} \\ $$
Commented by bemath last updated on 03/Jun/20
$$\int\:\frac{\mathrm{ln}\left(\mathrm{a}\right)}{\mathrm{x}\:\mathrm{ln}\left(\mathrm{x}\right)}\:\mathrm{dx}\:=\:\mathrm{ln}\left(\mathrm{a}\right)\:\int\:\frac{\mathrm{du}}{\mathrm{u}} \\ $$$$=\:\mathrm{ln}\left(\mathrm{a}\right)\:\mathrm{ln}\left(\mathrm{u}\right)\:+\:\mathrm{c}\: \\ $$$$=\:\mathrm{ln}\left(\mathrm{a}\right)\:\mathrm{ln}\left(\mathrm{ln}\left(\mathrm{x}\right)\right)\:+\:\mathrm{c}\: \\ $$