Question Number 68699 by Rio Michael last updated on 15/Sep/19 $$\int\:{ln}\left({x}\:+\:\mathrm{4}\right)\:{dx}\:= \\ $$ Commented by mathmax by abdo last updated on 15/Sep/19 $${let}\:{I}\:=\int{ln}\left({x}+\mathrm{4}\right){dx}\:\:{changement}\:{x}+\mathrm{4}={t}\:{give} \\ $$$${I}\:=\int{lnt}\:{dt}\:={tln}\left({t}\right)−{t}\:+{c}\:=\left({x}+\mathrm{4}\right){ln}\left({x}+\mathrm{4}\right)−{x}−\mathrm{4}\:+{c}…
Question Number 134239 by ruwedkabeh last updated on 01/Mar/21 $${can}\:{i}\:{ask}\:{for}\:{some}\:{help}? \\ $$$${how}\:{to}\:{prove}\:{this}? \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}<\underset{\mathrm{0}} {\overset{\frac{\mathrm{1}}{\mathrm{2}}} {\int}}\frac{{dx}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{3}} }}<\frac{\pi}{\mathrm{6}} \\ $$ Commented by Dwaipayan Shikari last updated…
Question Number 134227 by Raxreedoroid last updated on 01/Mar/21 $$\mathrm{I}\:\:\mathrm{struck}\:\mathrm{upon}\:\mathrm{this} \\ $$$$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\mathrm{16}^{{n}} =\frac{−\mathrm{1}}{\mathrm{15}} \\ $$$$\int_{\mathrm{0}} ^{\:\pi} \mathrm{cos}^{\mathrm{4}} \:{x}\:\mathrm{sin}\:{x}\:{dx}=\frac{−\mathrm{1}}{\mathrm{5}}\left[\mathrm{cos}^{\mathrm{5}} \:{x}\right]_{\mathrm{0}} ^{\pi} =\mathrm{0}.\mathrm{4} \\ $$$$\mathrm{in}\:\mathrm{another}\:\mathrm{way}…
Question Number 134219 by Raxreedoroid last updated on 01/Mar/21 $$\int_{\mathrm{0}} ^{\:\pi} \mathrm{cos}^{\mathrm{4}} \:{x}\:\mathrm{sin}\:{x}\:{dx}=? \\ $$ Answered by liberty last updated on 01/Mar/21 $$=−\left[\frac{\mathrm{1}}{\mathrm{5}}\mathrm{cos}\:^{\mathrm{5}} \mathrm{x}\:\right]_{\mathrm{0}} ^{\pi}…
Question Number 68660 by aliesam last updated on 14/Sep/19 $$\int{e}^{{x}+{e}^{{x}} } \:{dx} \\ $$ Commented by aliesam last updated on 14/Sep/19 $${perfect} \\ $$ Commented…
Question Number 134185 by mnjuly1970 last updated on 28/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:…..{advanced}\:\:\:{calculus}…. \\ $$$$\:\:\:\:{prove}\:\:{that}:: \\ $$$$\:\:\:\:\:{i}:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{{cos}\left({tan}\left({x}\right)−{x}\right)}{{cos}\left({x}\right)}{dx}=\frac{\pi}{{e}} \\ $$$$\:\:\:\:{ii}:\underset{{n}=\mathrm{2}} {\overset{\infty} {\prod}}{e}\left(\mathrm{1}−\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\right)^{{n}^{\mathrm{2}} } =\frac{\pi}{{e}\sqrt{{e}}} \\ $$$$\:\:…
Question Number 134182 by Algoritm last updated on 28/Feb/21 Answered by Ñï= last updated on 01/Mar/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}\right)^{\mathrm{3}} \frac{\left(\mathrm{1}+{x}\right)}{\left(\mathrm{1}−{x}\right)\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{dx} \\ $$$$=\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 68600 by Abdo msup. last updated on 14/Sep/19 $$\left.\mathrm{1}\right){calculatef}\left({a}\right)=\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({arctanx}\right)}{{a}+{x}^{\mathrm{2}} }{dx}\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)?{calculste}\:\:{g}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\frac{{cos}\left({arctanx}\right)}{\left({a}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right){find}\:{the}\:{value}\:{if}\:{integrals} \\ $$$$\int_{\mathrm{0}} ^{\infty}…
Question Number 68598 by Abdo msup. last updated on 14/Sep/19 $$\:{find}\:\int\:\:\:\:\frac{{dx}}{{x}^{\mathrm{3}} −\mathrm{4}{x}\:+\mathrm{3}} \\ $$ Commented by turbo msup by abdo last updated on 14/Sep/19 $${let}\:{I}\:=\int\:\:\frac{{dx}}{{x}^{\mathrm{3}}…
Question Number 68596 by Abdo msup. last updated on 14/Sep/19 $${calculate}\:\int_{\frac{\pi}{\mathrm{2}}} ^{\frac{\pi}{\mathrm{3}}} \:\:\:\:\frac{{xdx}}{\mathrm{3}+{cosx}} \\ $$ Commented by mathmax by abdo last updated on 15/Sep/19 $${changeent}\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}\:{give}…