Question Number 8691 by FilupSmith last updated on 22/Oct/16 $$\int_{\mathrm{0}} ^{\:\infty} {x}^{−\mathrm{ln}\left({x}\right)} {dx} \\ $$ Commented by FilupSmith last updated on 22/Oct/16 $${x}^{−\mathrm{ln}\left({x}\right)} ={e}^{−\mathrm{ln}\left({x}\right)\mathrm{ln}\left({x}\right)} ={e}^{−\mathrm{ln}^{\mathrm{2}}…
Question Number 74223 by mathmax by abdo last updated on 20/Nov/19 $${calculate}\:\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{{x}^{\mathrm{2}} +{ax}+\mathrm{1}}{dx}\:\:\:{and}\:{g}\left({a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{xdx}}{\:\sqrt{{x}^{\mathrm{2}} +{ax}+\mathrm{1}}} \\ $$$${with}\:\:\mid{a}\mid<\mathrm{2} \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{{x}^{\mathrm{2}} +\sqrt{\mathrm{2}}{x}+\mathrm{1}}{dx}\:{and}\:\int_{\mathrm{0}}…
Question Number 74218 by malikmasood3535@gmail.com last updated on 20/Nov/19 $${verify}\:{that}\:{y}\left({x}\right)={e}^{{x}} \left(\mathrm{cos}\:{e}^{{x}} −{e}^{{x}} \mathrm{sin}\:{e}^{{x}} \right)\:{is}\:{the}\:{solution}\:{of}\:{integral}\:{equation}\:{y}\left({x}\right)=\left(\mathrm{1}−{xe}^{\mathrm{2}{x}} \right)\mathrm{cos}\:\mathrm{1}−{e}^{\mathrm{2}{x}} \mathrm{sin}\:\mathrm{1}+\underset{\mathrm{0}} {\overset{{x}} {\int}}\left\{\mathrm{1}−\left({x}−{t}\right){e}^{\mathrm{2}{x}} \right\}{y}\left({t}\right){dt} \\ $$ Answered by mind is…
Question Number 139750 by bramlexs22 last updated on 01/May/21 $$\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\left(\left(\mathrm{1}−\mathrm{x}^{\mathrm{7}} \right)^{\mathrm{1}/\mathrm{3}} \:\left(\mathrm{1}−\mathrm{x}^{\mathrm{3}} \right)^{\mathrm{1}/\mathrm{7}} \:\right)\mathrm{dx}\:=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 74210 by malikmasood3535@gmail.com last updated on 20/Nov/19 $$\int{e}^{{t}} \mathrm{cos}\:{e}^{{t}} {dt} \\ $$ Answered by mind is power last updated on 20/Nov/19 $$\int{e}^{{t}} {cos}\left({t}\right)\:{dt}={sin}\left({e}^{{t}}…
Question Number 139746 by mathlove last updated on 01/May/21 Answered by bramlexs22 last updated on 01/May/21 $$\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{x}\right)=\mathrm{t} \\ $$$$\:\Rightarrow\mathrm{t}+\frac{\mathrm{1}}{\mathrm{t}}\:=\:\mathrm{e}+\mathrm{e}^{−\mathrm{1}} \\ $$$$\Rightarrow\mathrm{t}^{\mathrm{2}} −\left(\mathrm{e}+\mathrm{e}^{−\mathrm{1}} \right)\mathrm{t}+\mathrm{1}=\mathrm{0} \\…
Question Number 8672 by swapnil last updated on 20/Oct/16 $$\underset{\mathrm{0}} {\overset{\infty} {\int}}\mathrm{x}.\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} } \:\mathrm{dx} \\ $$$$\mathrm{evaluate}\:\mathrm{above}\:\mathrm{expression}. \\ $$ Answered by 123456 last updated on 21/Oct/16…
Question Number 139734 by mnjuly1970 last updated on 30/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…..\:{nice}\:…{calculus}….. \\ $$$$\:\:\:\:\:\:\:{calculate}\:::\:\: \\ $$$$\:\:\:\:\:\:\mathscr{F}\::=\:\int_{\mathrm{0}} ^{\:\infty} {te}^{−{t}} {sin}^{\mathrm{3}} \left({t}\right){dt}=? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:………………….. \\ $$ Answered…
Question Number 139708 by qaz last updated on 30/Apr/21 $${Prove}:\:\:\:\mathrm{1}+\mathrm{2}\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{a}^{{n}} \mathrm{cos}\:\left({nx}\right)=\frac{\mathrm{1}−{a}^{\mathrm{2}} }{\mathrm{1}−\mathrm{2}{a}\mathrm{cos}\:{x}+{a}^{\mathrm{2}} },\:\:\:\:\:\:\left(\mid{a}\mid<\mathrm{1}\right) \\ $$$${And}\:{calculate}::\:\:\int_{\mathrm{0}} ^{\pi} \frac{{x}^{\mathrm{2}} }{\mathrm{1}+\mathrm{8sin}\:^{\mathrm{2}} {x}}{dx}=\frac{\mathrm{5}\pi^{\mathrm{3}} }{\mathrm{36}}−\frac{\pi}{\mathrm{6}}{ln}^{\mathrm{2}} \mathrm{2} \\ $$…
Question Number 8632 by swapnil last updated on 19/Oct/16 $${evaluate} \\ $$$$\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}\underset{\mathrm{0}} {\overset{\mathrm{4}} {\int}}\mathrm{1}+{x}\:{dy}\:{dx} \\ $$$$\: \\ $$ Answered by FilupSmith last updated…