Question Number 7814 by Tawakalitu. last updated on 16/Sep/16 $$\int{x}\sqrt{\mathrm{2}{x}\:+\:\mathrm{1}}\:{dx}\: \\ $$ Commented by l-becker last updated on 17/Sep/16 $$ \\ $$$$\frac{{x}}{{dx}}\left(\sqrt{\mathrm{2}{x}+\mathrm{1}}\:\right) \\ $$$$\frac{{x}}{{dx}}\int\sqrt{\mathrm{4}{x}+\mathrm{1}}\:+{C} \\…
Question Number 73338 by mathmax by abdo last updated on 10/Nov/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left(\mathrm{2}{cosx}\right)}{\mathrm{3}+{x}^{\mathrm{2}} }{dx} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 73337 by mathmax by abdo last updated on 10/Nov/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{cos}\left({artan}\left(\mathrm{2}{x}\right)\right)}{\left(\mathrm{3}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx} \\ $$ Commented by mathmax by abdo last updated…
Question Number 73336 by mathmax by abdo last updated on 10/Nov/19 $${find}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{t}} {ln}\left(\mathrm{1}+{e}^{{t}} \right){dt} \\ $$ Commented by mathmax by abdo last updated…
Question Number 7798 by Tawakalitu. last updated on 16/Sep/16 $$\int\frac{{x}^{\mathrm{2}} }{\:\sqrt{{x}^{\mathrm{3}} \:+\:\mathrm{5}}}\:{dx} \\ $$ Commented by sou1618 last updated on 16/Sep/16 $$\frac{{d}}{{dx}}\left(\sqrt{{x}^{\mathrm{3}} +\mathrm{5}}\right)=\frac{\mathrm{3}{x}^{\mathrm{2}} }{\mathrm{2}\sqrt{{x}^{\mathrm{3}} +\mathrm{5}}}…
Question Number 73335 by mathmax by abdo last updated on 10/Nov/19 $${eplcit}\:\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left({x}+{t}+{t}^{\mathrm{2}} \right){dt}\:\:\:\:\:\:{with}\:{x}>\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left({t}^{\mathrm{2}} \:+{t}\:+\sqrt{\mathrm{2}}\right){dt} \\ $$ Commented by mathmax…
Question Number 73333 by mathmax by abdo last updated on 10/Nov/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{cos}\left(\pi\:+\mathrm{2}{x}^{\mathrm{2}} \right)}{\left({x}^{\mathrm{2}} \:+\mathrm{4}\right)^{\mathrm{2}} }{dx} \\ $$ Commented by mathmax by abdo last…
Question Number 7792 by Tawakalitu. last updated on 15/Sep/16 Commented by FilupSmith last updated on 16/Sep/16 $$\left(\mathrm{3}\right)\:\:\int_{\mathrm{1}} ^{\:\mathrm{3}} {x}\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}{dx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int_{{x}=\mathrm{1}} ^{\:{x}=\mathrm{3}} {x}\left({x}^{\mathrm{2}} −\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{2}}}…
Question Number 73331 by mathmax by abdo last updated on 10/Nov/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{ln}\left(\mathrm{1}+{e}^{−\mathrm{3}{x}^{\mathrm{2}} } \right)}{\mathrm{3}+{x}^{\mathrm{2}} }{dx} \\ $$ Commented by mathmax by abdo last…
Question Number 138860 by qaz last updated on 19/Apr/21 $${Prove}::\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{{x}^{\mathrm{3}} −\mathrm{sin}\:^{\mathrm{3}} {x}}{{x}^{\mathrm{5}} }{dx}=\frac{\mathrm{13}}{\mathrm{32}}\pi \\ $$ Answered by Dwaipayan Shikari last updated on 19/Apr/21…