Question Number 179496 by a.lgnaoui last updated on 29/Oct/22
$${Evaluer} \\ $$$$\int_{\mathrm{1}} ^{\mathrm{2}} \frac{\mathrm{sin}\:\left(\mathrm{log}\left(\mathrm{x}\right)\right)}{\mathrm{x}}\mathrm{dx} \\ $$
Answered by ARUNG_Brandon_MBU last updated on 29/Oct/22
![∫_1 ^2 ((sin(logx))/x)dx =∫_1 ^2 sin(logx)d(logx) =[cos(logx)]_2 ^1 =1−cos(log2)](https://www.tinkutara.com/question/Q179497.png)
$$\int_{\mathrm{1}} ^{\mathrm{2}} \frac{\mathrm{sin}\left(\mathrm{log}{x}\right)}{{x}}{dx} \\ $$$$=\int_{\mathrm{1}} ^{\mathrm{2}} \mathrm{sin}\left(\mathrm{log}{x}\right){d}\left(\mathrm{log}{x}\right) \\ $$$$=\left[\mathrm{cos}\left(\mathrm{log}{x}\right)\right]_{\mathrm{2}} ^{\mathrm{1}} =\mathrm{1}−\mathrm{cos}\left(\mathrm{log2}\right) \\ $$
Commented by a.lgnaoui last updated on 30/Oct/22
$${thanks} \\ $$