Question Number 86638 by M±th+et£s last updated on 29/Mar/20 $${I}=\int\frac{{x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} +\mathrm{7}{x}−\mathrm{1}}{\left({x}−\mathrm{3}\right)^{\mathrm{3}} \left({x}−\mathrm{2}\right)^{\mathrm{2}} }{dx} \\ $$ Answered by MJS last updated on 29/Mar/20 $$\frac{{x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}}…
Question Number 152175 by john_santu last updated on 26/Aug/21 $$\mathrm{what}\:\mathrm{exact}\:\mathrm{value}\:\mathrm{sin}\:\mathrm{2x}\:\mathrm{if}\:\mathrm{given} \\ $$$$\:\mathrm{cos}\:\mathrm{3x}\:=\:\frac{\mathrm{2}}{\:\sqrt{\mathrm{5}}} \\ $$ Commented by MJS_new last updated on 26/Aug/21 $$\mathrm{cos}\:\mathrm{3}{x}\:=\mathrm{4cos}^{\mathrm{3}} \:{x}\:−\mathrm{3cos}\:{x} \\ $$$$\mathrm{sin}\:\mathrm{2}{x}\:=\pm\mathrm{2cos}\:{x}\:\sqrt{\mathrm{1}−\mathrm{cos}^{\mathrm{2}}…
Question Number 21100 by ibraheem160 last updated on 12/Sep/17 $$\mathrm{if}\:\mathrm{3}^{\mathrm{2n}+\mathrm{3}} =\mathrm{m},\mathrm{find}\:\mathrm{3}^{−\mathrm{n}} \\ $$ Commented by chernoaguero@gmail.com last updated on 13/Sep/17 $$\mathrm{3}^{\mathrm{2}{n}} ×\mathrm{2}^{\mathrm{3}} ={m} \\ $$$$\mathrm{27}\left(\mathrm{3}^{{n}}…
Question Number 86634 by liki last updated on 29/Mar/20 Answered by MJS last updated on 29/Mar/20 $$\int\frac{\mathrm{cos}^{\mathrm{2}} \:\theta}{\mathrm{tan}\:\theta\:−\mathrm{1}}{d}\theta= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{tan}\:\theta\:\rightarrow\:{d}\theta=\mathrm{cos}^{\mathrm{2}} \:\theta\:{dt}\right] \\ $$$$=\int\frac{{dt}}{\left({t}−\mathrm{1}\right)\left({t}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }=…
Question Number 21097 by Tinkutara last updated on 12/Sep/17 $$\mathrm{Suppose}\:\mathrm{in}\:\mathrm{the}\:\mathrm{plane}\:\mathrm{10}\:\mathrm{pairwise} \\ $$$$\mathrm{nonparallel}\:\mathrm{lines}\:\mathrm{intersect}\:\mathrm{one}\:\mathrm{another}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{possible}\:\mathrm{number} \\ $$$$\mathrm{of}\:\mathrm{polygons}\:\left(\mathrm{with}\:\mathrm{finite}\:\mathrm{areas}\right)\:\mathrm{that}\:\mathrm{can} \\ $$$$\mathrm{be}\:\mathrm{formed}? \\ $$ Answered by Tinkutara last updated…
Question Number 152165 by peter frank last updated on 26/Aug/21 $$\int\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{sin}\:\mathrm{3x}}\mathrm{dx} \\ $$ Answered by john_santu last updated on 26/Aug/21 $$\:\mathrm{I}=\int\:\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{3sin}\:\mathrm{x}−\mathrm{4sin}\:^{\mathrm{3}} \mathrm{x}}\:\mathrm{dx}\: \\ $$$$\mathrm{I}=\int\:\frac{\mathrm{dx}}{\mathrm{3}−\mathrm{4sin}\:^{\mathrm{2}} \mathrm{x}}…
Question Number 152164 by peter frank last updated on 26/Aug/21 $$\int\frac{\mathrm{2x}+\mathrm{1}}{\mathrm{4}−\mathrm{3x}−\mathrm{x}^{\mathrm{2}} }\mathrm{dx} \\ $$ Commented by Paradoxical last updated on 26/Aug/21 Commented by peter frank…
Question Number 152161 by peter frank last updated on 26/Aug/21 $$\int\mathrm{cos}\:\left(\mathrm{log}\:\mathrm{x}\right)\mathrm{dx} \\ $$ Answered by Olaf_Thorendsen last updated on 26/Aug/21 $$\mathrm{F}\left({x}\right)\:=\:\int\mathrm{cos}\left(\mathrm{log}{x}\right)\:{dx} \\ $$$$\mathrm{F}\left({e}^{{u}} \right)\:=\:\int\mathrm{cos}{u}\:{e}^{{u}} {du}…
Question Number 86626 by sakeefhasan05@gmail.com last updated on 29/Mar/20 $$\int\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{4}}\:\:\mathrm{dx} \\ $$$$\mathrm{answer}\:\mathrm{quick}\:\mathrm{pls} \\ $$ Commented by sakeefhasan05@gmail.com last updated on 30/Mar/20 Commented by mathmax…
Question Number 152160 by peter frank last updated on 26/Aug/21 $$\int\left[\frac{\mathrm{1}}{\mathrm{log}\:\mathrm{x}}−\frac{\mathrm{1}}{\left(\mathrm{log}\:\mathrm{x}\right)^{\mathrm{2}} }\right]\mathrm{dx} \\ $$ Answered by Olaf_Thorendsen last updated on 26/Aug/21 $$\mathrm{F}\left({x}\right)\:=\:\int\left(\frac{\mathrm{1}}{\mathrm{log}{x}}−\frac{\mathrm{1}}{\mathrm{log}^{\mathrm{2}} {x}}\right){dx} \\ $$$$\mathrm{F}\left({x}\right)\:=\:\int\frac{\mathrm{log}{x}−\mathrm{1}}{\mathrm{log}^{\mathrm{2}}…