Question Number 104826 by Study last updated on 24/Jul/20
$$\int\mathrm{3}^{{x}+\mathrm{2}} \centerdot{lnsin}\mathrm{3}^{{x}} {dx}=??? \\ $$
Commented by Study last updated on 24/Jul/20
$${help}\:{me} \\ $$
Answered by Dwaipayan Shikari last updated on 24/Jul/20
$$\mathrm{3}^{\mathrm{2}} \int\mathrm{3}^{{x}} {log}\left({sin}\mathrm{3}^{{x}} \right){dx} \\ $$$$\frac{\mathrm{3}^{\mathrm{2}} }{{log}\mathrm{3}}\int{ulog}\left({sinu}\right) \\ $$$$\frac{\mathrm{9}}{{log}\mathrm{3}}{log}\left({sinu}\right)\frac{{u}^{\mathrm{2}} }{\mathrm{2}}−\frac{\mathrm{9}}{\mathrm{2}{log}\mathrm{3}}\int{u}^{\mathrm{2}} {cotu}……{continue} \\ $$