Question Number 65776 by mathmax by abdo last updated on 03/Aug/19
$${find}\:\:\int_{−\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{cosx}}{\mathrm{2}+\mathrm{5}{sinx}}{dx} \\ $$
Commented by kaivan.ahmadi last updated on 04/Aug/19
$${u}=\mathrm{2}+\mathrm{5}{sinx}\Rightarrow{du}=\mathrm{5}{cosxdx} \\ $$$$\frac{\mathrm{1}}{\mathrm{5}}\int\frac{{du}}{{u}}=\frac{\mathrm{1}}{\mathrm{5}}{lnu}=\frac{\mathrm{1}}{\mathrm{5}}{ln}\left(\mathrm{2}+\mathrm{5}{sinx}\right)\mid_{−\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{4}}} = \\ $$