Question Number 125133 by mnjuly1970 last updated on 08/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…\:\blacktriangleleft{advanced}\:\:\:{calculus}\blacktriangleright… \\ $$$$\:\:\:\:\:\:{prove}\:\:{that}\:::: \\ $$$$\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\mathrm{1}} \left\{\frac{{cos}\left({log}\left({x}\right)\right)−\mathrm{1}}{{log}\left({x}\right)}\right\}{dx}=\frac{{log}\left(\mathrm{2}\right)}{\mathrm{2}} \\ $$$$\:\:\:\:\:\:…\ast{adopted}\:{from}\:{youtube}\ast…\:\:\: \\ $$$$\:\ast\:\ast\:{youtube}\:{solution}\:{is}\:{not}\:{considered}\:\ast\:\ast \\ $$$$\:\: \\ $$ Answered…
Question Number 125125 by Study last updated on 08/Dec/20 $$\underset{\frac{\pi}{\mathrm{6}}} {\int}\frac{\overset{\frac{\pi}{\mathrm{3}}} {{s}inx}\:}{{x}}{dx}=? \\ $$ Commented by Dwaipayan Shikari last updated on 08/Dec/20 $${Si}\left(\frac{\pi}{\mathrm{3}}\right)−{Si}\left(\frac{\pi}{\mathrm{6}}\right) \\ $$…
Question Number 125114 by bramlexs22 last updated on 08/Dec/20 $$\:{solve}\:\int\:\frac{{dx}}{\left({x}^{\mathrm{3}} −\mathrm{1}\right)^{\mathrm{2}} }\:? \\ $$ Commented by liberty last updated on 08/Dec/20 $${Ostrogradsky}'{s}\:{method}\:\left(\:{Prof}\:{sir}\:{MJS}\:\right) \\ $$ Answered…
let-f-x-dt-x-t-t-2-x-2-1-determine-a-explicit-form-of-f-x-2-determine-dt-x-2-t-2-4-and-dt-x-1-t-2-1-
Question Number 59576 by maxmathsup by imad last updated on 12/May/19 $${let}\:{f}\left({x}\right)\:=\int\:\:\:\:\:\:\:\frac{{dt}}{\left({x}+{t}\right)\sqrt{{t}^{\mathrm{2}} −{x}^{\mathrm{2}} }} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{determine}\:\int\:\:\:\:\:\frac{{dt}}{\left({x}+\mathrm{2}\right)\sqrt{{t}^{\mathrm{2}} −\mathrm{4}}}\:\:{and}\:\:\int\:\:\:\:\:\:\frac{{dt}}{\left({x}+\mathrm{1}\right)\sqrt{{t}^{\mathrm{2}} −\mathrm{1}}} \\ $$ Commented by tanmay…
Question Number 59575 by maxmathsup by imad last updated on 12/May/19 $${find}\:\int\:\:\frac{{sin}\left(\mathrm{2}{x}\right)}{\mathrm{1}+{cos}^{\mathrm{2}} {x}}{dx} \\ $$ Answered by Smail last updated on 12/May/19 $$\int\frac{{sin}\left(\mathrm{2}{x}\right)}{\mathrm{1}+{cos}^{\mathrm{2}} {x}}{dx}=\int\frac{{sin}\left(\mathrm{2}{x}\right)}{\mathrm{1}+\frac{\mathrm{1}+{cos}\mathrm{2}{x}}{\mathrm{2}}}{dx} \\…
Question Number 59563 by aliesam last updated on 11/May/19 Commented by aliesam last updated on 11/May/19 $${thank}\:{you}\:{sir} \\ $$ Answered by MJS last updated on…
Question Number 125098 by mnjuly1970 last updated on 08/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:\:{calculus}\:… \\ $$$$\:\:\:\:\:{prove}\:\:{that}\:::\:{Apery}'{s}\:{constant} \\ $$$$\:\:\:\:\:\phi=\int_{\mathrm{0}} ^{\:\mathrm{1}} \left\{\left(\mathrm{4}{x}^{\mathrm{2}} +\mathrm{4}^{\mathrm{2}} {x}^{\mathrm{2}^{\mathrm{2}} } +\mathrm{4}^{\mathrm{3}} {x}^{\mathrm{2}^{\mathrm{3}} } +…\right)\frac{{ln}^{\mathrm{2}} \left({x}\right)}{{x}\left(\mathrm{1}+{x}\right)}\right\}{dx} \\…
Question Number 125096 by mnjuly1970 last updated on 08/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:…\:{nice}\:\:\:{calculus}… \\ $$$$\:\:\:\:{suppose}\:::\:{z}\:={x}−{iy}\:\:\&\:\sqrt[{\mathrm{3}}]{{z}}\:={p}+{iq} \\ $$$$\:\:\:{then}\:\:{find}\:::\:\:\:{A}=\frac{\frac{{x}}{{p}}+\frac{{y}}{{q}}}{{p}^{\mathrm{2}} +{q}^{\mathrm{2}} }\:=?? \\ $$$$\:{note}\::\:{i}=\sqrt{−\mathrm{1}} \\ $$ Answered by MJS_new last updated…
Question Number 190624 by Rupesh123 last updated on 07/Apr/23 Answered by mr W last updated on 07/Apr/23 Commented by mr W last updated on 07/Apr/23…
Question Number 190623 by mnjuly1970 last updated on 07/Apr/23 $$ \\ $$$$\:\:\:\:\:\:\mathrm{calculate}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\left(−\mathrm{1}\right)^{\:{n}−\mathrm{1}} }{{n}}\:\mathrm{cos}\:\left(\frac{\:{n}\pi}{\mathrm{3}}\:\right)\:=? \\ $$$$ \\ $$ Answered by…