Question Number 64200 by aliesam last updated on 15/Jul/19 Commented by mathmax by abdo last updated on 15/Jul/19 $${let}\:{I}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{x}−\mathrm{1}}{{lnx}}{dx}\:{changement}\:{lnx}=−{t}\:{give}\:{x}={e}^{−{t}} \\ $$$${I}\:=−\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−{t}}…
Question Number 64176 by aliesam last updated on 15/Jul/19 Answered by MJS last updated on 15/Jul/19 $$\mathrm{the}\:\mathrm{minimum}\:\mathrm{of}\:{f}\left({x}\right)=\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:\mathrm{is}\:{f}\left(\mathrm{0}\right)=\mathrm{1}\:\Rightarrow\:\mathrm{the} \\ $$$$\mathrm{area}\:\mathrm{between}\:\mathrm{the}\:{x}−\mathrm{axis}\:\mathrm{and}\:{f}\left({x}\right)\:\mathrm{in}\:\left[−\mathrm{1};\:\mathrm{1}\right] \\ $$$$\mathrm{is}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{2}\:\Rightarrow\:\mathrm{2}<\underset{−\mathrm{1}} {\int}^{\mathrm{1}} \sqrt{\mathrm{1}+{x}^{\mathrm{2}} }{dx}…
Question Number 64166 by mathmax by abdo last updated on 14/Jul/19 $${calculate}\:\:{A}_{{n}} =\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}} \:+\mathrm{2}\right)….\left({x}^{\mathrm{2}} \:+{n}\right)} \\ $$$${with}\:{n}\:{integr}\:{natural}\:\:{and}\:{n}\geqslant\mathrm{1} \\ $$ Answered by Eminem…
Question Number 64160 by mathmax by abdo last updated on 14/Jul/19 $${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{dt}}{{x}\:+\mathrm{2}^{{t}} }\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:{for}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{also}\:{g}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{dt}}{\left({x}+\mathrm{2}^{{x}} \right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:{give}\:{f}^{\left({n}\right)}…
Question Number 129696 by Eric002 last updated on 17/Jan/21 $${nice}\:{old}\:{question}\:{by}\:{sir}\:{m}?{th}+{et}?{s}\: \\ $$$$\int_{\mathrm{0}} ^{\infty} {cos}\left(\frac{{x}^{\mathrm{3}} }{\mathrm{3}}+{tx}\right){dx} \\ $$$$ \\ $$ Commented by mathdave last updated on…
Question Number 64159 by mathmax by abdo last updated on 14/Jul/19 $${calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dx}}{\mathrm{3}+\mathrm{2}^{{x}} } \\ $$ Commented by turbo msup by abdo last updated…
Question Number 129688 by Engr_Jidda last updated on 17/Jan/21 $${complex}\:{analysis} \\ $$$$\oint_{{C}} \frac{\varrho^{\mathrm{2}{z}} +{sinz}^{\mathrm{2}} }{\left({z}−\mathrm{2}\right)\left({z}−\mathrm{3}\right)}{dz}\:\:\:{C}:\mid{Z}\mid=\mathrm{5} \\ $$ Answered by mathmax by abdo last updated on…
Question Number 64150 by mathmax by abdo last updated on 14/Jul/19 $${calculate}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{2}\right)\left({x}^{\mathrm{2}} +\mathrm{3}\right)} \\ $$ Commented by mathmax by abdo last…
Question Number 129684 by mnjuly1970 last updated on 17/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{advanced}\:\:{calculus}… \\ $$$$\:\:{prove}\:\:{that}: \\ $$$$\:\:\int_{\mathrm{0}} ^{\:\pi} {cos}\left({tan}\left({x}\right)−{cot}\left({x}\right)\right){dx}=\frac{\pi}{{e}^{\mathrm{2}} } \\ $$$$ \\ $$ Answered by mindispower last…
Question Number 64147 by aliesam last updated on 14/Jul/19 Answered by ajfour last updated on 14/Jul/19 $$=\mathrm{sin}\:{y}−\mathrm{cos}\:{y}+{c} \\ $$ Answered by som(math1967) last updated on…