Question Number 114103 by gab last updated on 17/Sep/20 $$\int\sqrt{{ln}\left({tan}\left({x}\right)\right)}{dx} \\ $$ Commented by MJS_new last updated on 17/Sep/20 $$\mathrm{seems}\:\mathrm{unsolveable}\:\mathrm{to}\:\mathrm{me} \\ $$ Terms of Service…
Question Number 114094 by Lordose last updated on 17/Sep/20 $$\int\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{sin}}^{−\mathrm{1}} \left(\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{dx}} \\ $$ Answered by Olaf last updated on 17/Sep/20 $${u}'\:=\:\mathrm{ln}{x},\:{u}\:=\:{x}\mathrm{ln}{x}−{x} \\ $$$${v}\:=\:\mathrm{arcsin}{x},\:{v}'\:=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }} \\…
Question Number 114072 by Lordose last updated on 17/Sep/20 $$\int\frac{\mathrm{1}}{\boldsymbol{\mathrm{sinx}}\:+\:\boldsymbol{\mathrm{cosx}}}\boldsymbol{\mathrm{dx}} \\ $$ Answered by Olaf last updated on 17/Sep/20 $${x}\:=\:\frac{\pi}{\mathrm{4}}−{u} \\ $$$$\mathrm{sin}{x}+\mathrm{cos}{x}\:=\: \\ $$$$\left(\mathrm{sin}\frac{\pi}{\mathrm{4}}\mathrm{cos}{u}−\mathrm{sin}{u}\mathrm{cos}\frac{\pi}{\mathrm{4}}\right)+\left(\mathrm{cos}\frac{\pi}{\mathrm{4}}\mathrm{cos}{u}+\mathrm{sin}\frac{\pi}{\mathrm{4}}\mathrm{sin}{u}\right) \\…
Question Number 114056 by mathmax by abdo last updated on 16/Sep/20 $$\mathrm{calculate}\:\int_{\mathrm{2}} ^{+\infty} \:\:\:\:\frac{\mathrm{dt}}{\left(\mathrm{2t}+\mathrm{3}\right)^{\mathrm{4}} \left(\mathrm{t}−\mathrm{1}\right)^{\mathrm{5}} } \\ $$ Answered by Olaf last updated on 17/Sep/20…
Question Number 114044 by Her_Majesty last updated on 16/Sep/20 $${old}\:{and}\:{unanswered}…\:{Mr}\:{Mathdave}??? \\ $$$$\int{x}^{\mathrm{2}} {ln}\left(\mathrm{1}−{x}\right){ln}\left(\mathrm{1}+{x}\right){dx}=? \\ $$ Answered by mathdave last updated on 17/Sep/20 $${sokution} \\ $$$${put}\:{x}=\left(\mathrm{2}{y}−\mathrm{1}\right)\:\:\left({wat}\:{i}\:{did}\:{here}\:{is}\:{logical}\right)…
Question Number 114045 by mnjuly1970 last updated on 17/Sep/20 $$\:\:\:\:\:\:\:\:…\:\:{advanced}\:{calculus}… \\ $$$$ \\ $$$${i}\::\:\:{prove}\:\:{that}\::: \\ $$$$\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left(\mathrm{1}+{ln}\left(\mathrm{1}−{x}\right)\right)}{{ln}\left(\mathrm{1}−{x}\right)}\:{dx}\:\overset{?} {=}\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\Gamma\left({n}+\mathrm{1}\right)}{{n}^{\mathrm{2}} }\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$${ii}:\: \\…
Question Number 48498 by maxmathsup by imad last updated on 24/Nov/18 $${find}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{cos}^{{n}} {xdx}\:\:{and}\:{B}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{sin}^{{n}} {xdx} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{cos}^{\mathrm{6}} {xdx}\:{and}\:\int_{\mathrm{0}}…
Question Number 48497 by maxmathsup by imad last updated on 24/Nov/18 $${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{ln}\left(\mathrm{1}+{xt}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{xplicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}\: \\ $$$$\left.\mathrm{3}\right){find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{2}}…
Question Number 48496 by maxmathsup by imad last updated on 24/Nov/18 $${find}\:{f}\left({x}\right)\:=\int\:\:\frac{{ln}\left(\mathrm{1}+{xt}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 48495 by maxmathsup by imad last updated on 24/Nov/18 $$\left.\mathrm{1}\right){calculate}\:\:{I}\:=\int\:\frac{{ln}\left(\mathrm{1}+{t}\right)}{\mathrm{1}+{t}}{dt} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{ln}\left(\mathrm{1}+{t}\right)}{\mathrm{1}+{t}}{dt} \\ $$ Commented by maxmathsup by imad last updated…