Question Number 115169 by bobhans last updated on 24/Sep/20 $$\int\:\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{ln}\:{x}\right)\:{dx}\: \\ $$ Answered by bobhans last updated on 24/Sep/20 Answered by Bird last updated…
Question Number 180680 by cortano1 last updated on 15/Nov/22 Answered by ARUNG_Brandon_MBU last updated on 16/Nov/22 $${I}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}−\mathrm{1}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}{{x}+\mathrm{1}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}{dx},\:{x}=\mathrm{sinh}\theta \\ $$$$\:\:\:=\int_{\mathrm{0}} ^{\mathrm{ln}\left(\mathrm{1}+\sqrt{\mathrm{2}}\right)} \frac{\mathrm{sinh}\theta−\mathrm{1}+\mathrm{cosh}\theta}{\mathrm{sinh}\theta+\mathrm{1}+\mathrm{cosh}\theta}\left(\mathrm{cosh}\theta{d}\theta\right)…
Question Number 115111 by mnjuly1970 last updated on 23/Sep/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…{mathematical}\:\:{analysis}…\:\:\:\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{prove}\:\:{that}: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\left({x}^{\mathrm{8}} +\mathrm{1}\right){ln}\left({x}\right)}{{x}^{\mathrm{10}} −\mathrm{1}}\:{dx}=\frac{\pi^{\mathrm{2}} \varphi^{\mathrm{2}} }{\mathrm{25}}\:\:\checkmark \\…
Question Number 115071 by bemath last updated on 23/Sep/20 $$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{\mathrm{cos}\:{x}}{\:\sqrt{\mathrm{1}−\mathrm{sin}\:{x}}}\:{dx}\:? \\ $$ Answered by Dwaipayan Shikari last updated on 23/Sep/20 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{cosx}}{\:\sqrt{\mathrm{1}−{sinx}}}{dx}…
Question Number 115058 by mnjuly1970 last updated on 23/Sep/20 $$\:\:\:\:\:\:\:….\:\:{nice}\:\:{calculus}\:… \\ $$$$\:\:\:\:\:\:{a}\:,\:{b}\:,\:{c}\:,\:{d}\:\:\in\mathbb{N}\:{and}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}+\frac{\mathrm{1}}{{c}}+\frac{\mathrm{1}}{{d}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{find}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{max}\left({a}+{b}+{c}+{d}\right)\:=??? \\ $$$$\:\:\:\:\:\:…{m}.{n}.{july}.\mathrm{1970}… \\ $$ Answered…
Question Number 115055 by mnjuly1970 last updated on 23/Sep/20 $$\:\:\:\:\:\:\:\:\:\:\:…\:\:{nice}\:\:{calculus}… \\ $$$$\:\:\:\:\:\:\:\:{evaluation}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\chi=\int_{\mathrm{0}} ^{\:\mathrm{1}} {log}\left(\mathrm{1}−{x}\right).{log}\left(\mathrm{1}+{x}\right)\:=??? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{m}.{n}.{july}.\mathrm{197}{o}… \\ $$$$\: \\ $$ Answered…
Question Number 115051 by gab last updated on 23/Sep/20 $$\int{x}^{\mathrm{2}} \sqrt{{x}^{\mathrm{2}} −\mathrm{2}}{dx} \\ $$ Commented by Dwaipayan Shikari last updated on 23/Sep/20 $$\int\mathrm{2}\sqrt{\mathrm{2}}{sin}^{\mathrm{2}} \theta{cos}\theta\sqrt{\mathrm{2}{sin}^{\mathrm{2}} \theta−\mathrm{2}}\:{d}\theta\:\:\:\:\:\:\:\:\:\:\:{x}=\sqrt{\mathrm{2}}{sin}\theta\:\Rightarrow\mathrm{1}=\sqrt{\mathrm{2}}\:{cos}\theta\frac{{d}\theta}{{dx}}\:…
Question Number 115030 by bobhans last updated on 23/Sep/20 $$\underset{−\frac{\pi}{\mathrm{2}}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\sqrt{\mathrm{sec}\:{x}−\mathrm{cos}\:{x}}\:{dx}\:=? \\ $$ Answered by bemath last updated on 23/Sep/20 $$\underset{−\frac{\pi}{\mathrm{2}}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\sqrt{\frac{\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} {x}}{\mathrm{cos}\:{x}}}\:{dx}\:=\:\underset{−\frac{\pi}{\mathrm{2}}}…
Question Number 115026 by jm2bok last updated on 23/Sep/20 $$\mathrm{Solve}:\:\:\int_{\mathrm{1}/\pi} ^{\mathrm{1}/\mathrm{2}} \mathrm{ln}\:\lfloor\frac{\mathrm{1}}{{x}}\rfloor{dx} \\ $$ Answered by PRITHWISH SEN 2 last updated on 23/Sep/20 $$\mathrm{when} \\…
Question Number 115009 by arcana last updated on 22/Sep/20 $$\int_{\mathrm{C}} \frac{{e}^{{z}} }{\mathrm{1}−\mathrm{cos}\:{z}}{dz}\:;\:\mathrm{C}:\mid{z}\mid=\mathrm{1} \\ $$ Answered by Olaf last updated on 24/Sep/20 $$ \\ $$$$\int_{\mathrm{C}} \frac{\mathrm{co}{z}+{i}\mathrm{sin}{z}}{\mathrm{1}−\mathrm{cos}{z}}{dz}…