Question Number 110858 by mathdave last updated on 31/Aug/20
$${evaluate} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}\mathrm{ln}\left(\mathrm{1}+{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}}{dx} \\ $$$$\int_{\mathrm{0}} ^{\infty} \sqrt{\mathrm{1}+{x}^{\mathrm{6}} }{dx} \\ $$