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 \\ $$ Answered by Dwaipayan Shikari last updated on 19/Apr/21…
Question Number 73293 by ~blr237~ last updated on 10/Nov/19 $${Explicit}\:\:{f}\left({x}\right)=\:\int_{\mathrm{1}} ^{\infty} \:\frac{{lnt}}{\left({x}^{\mathrm{2}} +{t}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{dt}\: \\ $$ Commented by mathmax by abdo last updated on…
Question Number 138819 by qaz last updated on 18/Apr/21 $$\left(\mathrm{1}\right)::{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \mid{x}−\mathrm{2}{t}\mid{dt},\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{3}} {f}\left({x}\right){dx}=? \\ $$$$−−−−−−−−−−−−−−−−−−− \\ $$$$\left(\mathrm{2}\right)::{f}\left({x}\right)={x}^{\mathrm{2}} \centerdot\int_{\mathrm{1}} ^{{x}} \frac{{dt}}{{t}^{\mathrm{3}} −\mathrm{3}{t}^{\mathrm{2}} +\mathrm{3}{t}},\:\:\:\:\:\:\:\:\:\:\:\:\:{f}^{\left(\mathrm{2019}\right)} \left(\mathrm{1}\right)=? \\…
Question Number 73279 by byaw last updated on 09/Nov/19 Answered by mr W last updated on 09/Nov/19 $$\mathrm{40}={v}_{\mathrm{0}} ×\mathrm{4}+\frac{\mathrm{1}}{\mathrm{2}}{a}×\mathrm{4}^{\mathrm{2}} \\ $$$$\Rightarrow\mathrm{10}={v}_{\mathrm{0}} +\mathrm{2}{a}\:\:\:…\left({i}\right) \\ $$$$\mathrm{72}={v}_{\mathrm{0}} ×\mathrm{6}+\frac{\mathrm{1}}{\mathrm{2}}{a}×\mathrm{6}^{\mathrm{2}}…