Question Number 103198 by Dwaipayan Shikari last updated on 13/Jul/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} {sin}\left({logx}\right){dx} \\ $$ Commented by Dwaipayan Shikari last updated on 13/Jul/20 $${sinx}=\frac{{e}^{{ix}} −{e}^{−{ix}}…
Question Number 168732 by mnjuly1970 last updated on 16/Apr/22 Answered by mnjuly1970 last updated on 16/Apr/22 $$\:\:\:\:\:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:{x}^{\:\frac{\mathrm{1}}{\mathrm{4}}} +\:\mathrm{2}{x}^{\:\:\frac{\mathrm{5}}{\mathrm{4}}} +{x}^{\:\frac{\mathrm{9}}{\mathrm{4}}} }{\left(\mathrm{1}+{x}^{\:\mathrm{3}} \right)^{\:\mathrm{2}} }{dx} \\…
Question Number 103196 by bobhans last updated on 13/Jul/20 $$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\left(\frac{\mathrm{1}}{\mathrm{2}}−{x}\right)\:\mathrm{ln}\left(\mathrm{1}−{x}\right)\:{dx}}{{x}^{\mathrm{2}} −{x}+\mathrm{1}}\:? \\ $$ Answered by bramlex last updated on 13/Jul/20 $$\mathrm{replace}\:\mathrm{x}\:\mathrm{with}\:\mathrm{1}−\mathrm{x}\: \\ $$$$\mathrm{I}\:=\:\underset{\mathrm{0}}…
Question Number 37636 by math khazana by abdo last updated on 16/Jun/18 $${find}\:\:\int_{\mathrm{0}} ^{\mathrm{6}} \left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right){e}^{\left[−\mathrm{2}{x}\right]} {dx}\:. \\ $$ Commented by prof Abdo imad last…
Question Number 37635 by math khazana by abdo last updated on 16/Jun/18 $${let}\:{a}>\mathrm{0}\:\:{find}\:{the}\:{value}\:{of}\: \\ $$$${f}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{+\infty} \:{e}^{−\left({t}^{\mathrm{2}} \:\:+\frac{{a}}{{t}^{\mathrm{2}} }\right)} {dt}\: \\ $$ Commented by prof…
Question Number 37634 by math khazana by abdo last updated on 16/Jun/18 $${find}\:\int_{\mathrm{0}} ^{+\infty} \:\:{e}^{−\left({t}^{\mathrm{2}} \:+\frac{\mathrm{1}}{{t}^{\mathrm{2}} }\right)} {dt} \\ $$ Commented by prof Abdo imad…
Question Number 37633 by math khazana by abdo last updated on 16/Jun/18 $${find}\:\:\int_{\mathrm{0}} ^{+\infty} \left[\:\:{x}\:{e}^{−{x}} \right]{dx} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 16/Jun/18…
Question Number 168707 by safojontoshtemirov last updated on 16/Apr/22 Commented by safojontoshtemirov last updated on 16/Apr/22 $${help}\:{me} \\ $$ Answered by mindispower last updated on…
Question Number 37630 by math khazana by abdo last updated on 16/Jun/18 $${find}\:\:\int\:\:\:\:\:\:\:\:\frac{{dx}}{\:\sqrt{{x}}\:\:+\sqrt{{x}+\mathrm{1}}\:+\sqrt{{x}+\mathrm{2}}} \\ $$ Answered by Ahmed Neutron last updated on 16/Jun/18 $$\int\left(\frac{\sqrt{{x}}}{{dx}}\right)^{−\mathrm{1}} +\int\left(\frac{\sqrt{{x}+\mathrm{1}}}{{dx}}\right)^{−\mathrm{1}}…
Question Number 103154 by Dwaipayan Shikari last updated on 13/Jul/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} {logxlog}\left(\mathrm{1}−{x}\right){dx} \\ $$ Answered by OlafThorendsen last updated on 13/Jul/20 $$\mathrm{I}\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{ln}{x}\mathrm{ln}\left(\mathrm{1}−{x}\right){dx}…