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 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 $$\frac{{d}}{{dx}}\left(\sqrt{{x}^{\mathrm{3}} +\mathrm{5}}\right)=\frac{\mathrm{3}{x}^{\mathrm{2}} }{\mathrm{2}\sqrt{{x}^{\mathrm{3}} +\mathrm{5}}}…
Question Number 73332 by mathmax by abdo last updated on 10/Nov/19 $${let}\:{U}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:\frac{\left(−\mathrm{1}\right)^{{k}} }{\:\sqrt{\mathrm{2}{k}+\mathrm{1}}}\:\:{determine}\:{a}\:{equivalent}\:{of}\:{n}\:{when}\:{n}\rightarrow+\infty \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 73333 by mathmax by abdo last updated on 10/Nov/19 $${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} \\ $$ Commented by mathmax by abdo last…
Question Number 73330 by mathmax by abdo last updated on 10/Nov/19 $${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\frac{{ln}\left(\mathrm{2}−{cos}\left(\mathrm{2}{x}\right)\right)}{{ln}\left(\mathrm{1}+{xsin}\left(\mathrm{3}{x}\right)\right)} \\ $$ Commented by mathmax by abdo last updated on 11/Nov/19 $${let}\:{f}\left({x}\right)=\frac{{ln}\left(\mathrm{2}−{cos}\left(\mathrm{2}{x}\right)\right)}{{ln}\left(\mathrm{1}+{xsin}\left(\mathrm{3}{x}\right)\right)}\:{we}\:{have}\:{cos}\left(\mathrm{2}{x}\right)\sim\mathrm{1}−\frac{\left(\mathrm{2}{x}\right)^{\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 7792 by Tawakalitu. last updated on 15/Sep/16 Commented by FilupSmith last updated on 16/Sep/16 $$\left(\mathrm{3}\right)\:\:\int_{\mathrm{1}} ^{\:\mathrm{3}} {x}\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}{dx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int_{{x}=\mathrm{1}} ^{\:{x}=\mathrm{3}} {x}\left({x}^{\mathrm{2}} −\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{2}}}…
Question Number 7791 by Tawakalitu. last updated on 15/Sep/16 Commented by prakash jain last updated on 15/Sep/16 $$\mathrm{What}\:\mathrm{is}\:{d}\:\mathrm{in}\:\mathrm{the}\:\mathrm{question}\:\mathrm{above}? \\ $$ Commented by Chantria last updated…
Question Number 138860 by qaz last updated on 19/Apr/21 $${Prove}::\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{{x}^{\mathrm{3}} −\mathrm{sin}\:^{\mathrm{3}} {x}}{{x}^{\mathrm{5}} }{dx}=\frac{\mathrm{13}}{\mathrm{32}}\pi \\ $$ Answered by Dwaipayan Shikari last updated on 19/Apr/21…
Question Number 73327 by mathmax by abdo last updated on 10/Nov/19 $${let}\:{w}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{lnt}}{\left({x}^{\mathrm{2}} \:+{t}^{\mathrm{2}} \right)^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{1}\right)\:{explicit}\:{w}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:{U}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{{lnt}}{\left({n}^{\mathrm{2}} \:+{t}^{\mathrm{2}}…