Question Number 151983 by puissant last updated on 24/Aug/21 $$\int_{−\infty} ^{+\infty} \left(\frac{\mathrm{1}−{ix}}{\mathrm{1}+{ix}}\right)^{{n}} \left(\frac{\mathrm{1}+{ix}}{\mathrm{1}−{ix}}\right)^{{m}} \frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$ Answered by Olaf_Thorendsen last updated on 24/Aug/21 $$\mathrm{I}\:=\:\int_{−\infty}…
Question Number 20908 by j.masanja06@gmail.com last updated on 07/Sep/17 $${integrate}\:{with}\:{respect}\:{to}\:{x}\: \\ $$$$\int\left(\frac{\mathrm{2}{x}+\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{8}}\right){dx} \\ $$ Answered by Joel577 last updated on 07/Sep/17 $${I}\:=\:\int\:\frac{\mathrm{2}{x}\:+\:\mathrm{1}}{\left({x}\:+\:\mathrm{2}\right)^{\mathrm{2}} \:+\:\mathrm{4}}\:{dx} \\…
Question Number 20907 by DKumar last updated on 07/Sep/17 $${How}\:{many}\:{zeroes}\:\left(\mathrm{0}\right)\:{there}\:{in}\:\mathrm{1}×\mathrm{2}×\mathrm{3}×\mathrm{4}……….\mathrm{99}×\mathrm{100}\: \\ $$ Answered by dioph last updated on 07/Sep/17 $$\mathrm{zeros}\:\mathrm{in}\:\mathrm{number}\:=\:\mathrm{maximum}\:\mathrm{integer} \\ $$$${n}\:\mathrm{such}\:\mathrm{that}\:\mathrm{10}^{{n}} =\mathrm{2}^{{n}} \mathrm{5}^{{n}} \:\mathrm{divides}\:\mathrm{the}\:\mathrm{number}.…
Question Number 151979 by mathdanisur last updated on 24/Aug/21 $$\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left(\mathrm{1}+\mathrm{mx}\right)^{\boldsymbol{\mathrm{n}}} \:-\:\left(\mathrm{1}+\mathrm{nx}\right)^{\boldsymbol{\mathrm{m}}} }{\mathrm{x}^{\mathrm{2}} }\:=\:?\:\:;\:\:\mathrm{m};\mathrm{n}\in\mathbb{N} \\ $$ Answered by mr W last updated on 24/Aug/21 $$\left(\mathrm{1}+{mx}\right)^{{n}}…
Question Number 20905 by NECx last updated on 07/Sep/17 $$\int{e}^{{x}^{\mathrm{2}} } {dx} \\ $$ Commented by NECx last updated on 07/Sep/17 $${please}\:{help} \\ $$ Answered…
Question Number 151973 by ajfour last updated on 24/Aug/21 Commented by ajfour last updated on 24/Aug/21 $${OB}={OC}=\sqrt{{OA}}\:\:;\:{OM}=\mathrm{1} \\ $$$${yellow}\:{area}=\mathrm{1}/\mathrm{4}\:,\:{then}\:{find} \\ $$$${OB}={OC}\:={x}\:\:\:{or}\:\:{OA}={x}^{\mathrm{2}} . \\ $$ Answered…
Question Number 20903 by ANTARES_VY last updated on 07/Sep/17 Answered by Joel577 last updated on 07/Sep/17 $$\mathrm{Using}\:\mathrm{polynomial}\:\mathrm{division},\mathrm{we}\:\mathrm{got} \\ $$$${I}\:=\:\int\:{x}^{\mathrm{3}} \:−\:{x}^{\mathrm{2}} \:+\:\mathrm{4}{x}\:−\:\mathrm{4}\:+\:\frac{\mathrm{4}{x}\:+\:\mathrm{1}}{{x}^{\mathrm{2}} \:+\:{x}}\:{dx} \\ $$$$\:\:\:=\:\int\:{x}^{\mathrm{3}} \:−\:{x}^{\mathrm{2}}…
Question Number 151965 by mnjuly1970 last updated on 24/Aug/21 $$ \\ $$$$\:\:\:{x}\:,\:{y}\:\in\:\mathbb{R}\: \\ $$$$\:\:\:\:\:\:\&\:{sin}\left({x}\:\right)+\:{cos}\:\left({y}\:\right)\:=\mathrm{1} \\ $$$${then}\:\:{max}\:\left(\:{sin}\left({y}\right)\:+\:{cos}\:\left({x}\right)\:\right)\:=? \\ $$$$\:\:…. \\ $$ Answered by mr W last…
Question Number 86431 by M±th+et£s last updated on 28/Mar/20 $$\int\sqrt{{x}−\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\:}\:{dx} \\ $$ Answered by jagoll last updated on 28/Mar/20 $$\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\:=\:\mathrm{x}−\mathrm{t}\: \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{1}\:=\:\mathrm{x}^{\mathrm{2}}…
Question Number 86428 by jagoll last updated on 28/Mar/20 $$\int\:\:\frac{\mathrm{dx}}{\mathrm{a}\:\mathrm{cos}\:\mathrm{x}\:+\:\mathrm{b}\:\mathrm{sin}\:\mathrm{x}}? \\ $$ Commented by jagoll last updated on 28/Mar/20 $$\mathrm{standard}\:\mathrm{solving} \\ $$$$\mathrm{a}\:\mathrm{cos}\:\mathrm{x}\:+\:\mathrm{b}\:\mathrm{sin}\:\mathrm{x}\:=\:\mathrm{k}\:\mathrm{cos}\:\left(\mathrm{x}−\theta\right) \\ $$$$\int\:\frac{\mathrm{dx}}{\mathrm{k}\:\mathrm{cos}\:\left(\mathrm{x}−\theta\right)}\:=\:\frac{\mathrm{1}}{\mathrm{k}}\int\:\mathrm{sec}\:\left(\mathrm{x}−\theta\right)\:\mathrm{dx} \\…