Question Number 62414 by mathmax by abdo last updated on 20/Jun/19 $${find}\:\int\:\:\:\:\:\frac{{e}^{{x}} }{\:\sqrt{{e}^{\mathrm{2}{x}} −\mathrm{1}}}{dx} \\ $$ Answered by $@ty@m last updated on 20/Jun/19 $${Put}\:{e}^{{x}} ={t}…
Question Number 127948 by rs4089 last updated on 03/Jan/21 Answered by mathmax by abdo last updated on 04/Jan/21 $$\mathrm{A}_{\mathrm{N}} =\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{e}^{\mathrm{2}\pi\mathrm{x}} −\mathrm{1}}{\mathrm{e}^{\mathrm{2}\pi\mathrm{x}} +\mathrm{1}}\left(\frac{\mathrm{1}}{\mathrm{x}}−\frac{\mathrm{x}}{\mathrm{N}^{\mathrm{2}} \:+\mathrm{x}^{\mathrm{2}}…
Question Number 62413 by mathmax by abdo last updated on 20/Jun/19 $${calculate}\:\:{W}_{{n}} =\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{cos}^{{n}} {xdx}\:\:\:\left(\:{n}\:{from}\:{N}\right)\:{and}\:{J}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{sin}^{{n}} {xdx} \\ $$ Terms of Service…
Question Number 62412 by mathmax by abdo last updated on 20/Jun/19 $${calculate}\:\:{lim}_{{n}\rightarrow+\infty} \:\:\int_{\mathrm{0}} ^{{n}} \:\left(\mathrm{1}−\frac{{x}}{{n}}\right)^{{n}} {dx} \\ $$ Commented by mathmax by abdo last updated…
Question Number 62410 by mathmax by abdo last updated on 20/Jun/19 $$\:\:{prove}\:{that}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{t}} {ln}\left({t}\right)\:{dt}\:=−\gamma\:\:\:\:\:\:\:\left(\:\:\gamma\:{is}\:{the}\:{constant}\:{of}\:{euler}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 127944 by liberty last updated on 03/Jan/21 $$\:\mathrm{If}\:\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}\:=\:\frac{\mathrm{1}}{\mathrm{3}}\:\mathrm{then}\:\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}\:+\:\mathrm{cos}\:^{\mathrm{3}} \mathrm{x}\:=? \\ $$ Answered by mr W last updated on 03/Jan/21 $${p}_{{n}} =\mathrm{sin}^{{n}} \:{x}+\mathrm{cos}^{{n}}…
Question Number 127943 by liberty last updated on 03/Jan/21 $$\:\frac{\mathrm{dy}}{\mathrm{dx}}\:+\:\mathrm{x}\:\mathrm{cos}\:^{\mathrm{2}} \left(\mathrm{y}−\mathrm{x}\right)\:=\:\mathrm{1}\: \\ $$ Answered by bramlexs22 last updated on 03/Jan/21 Terms of Service Privacy Policy…
Question Number 127940 by bramlexs22 last updated on 03/Jan/21 $$\:\begin{cases}{\mathrm{3x}=\mathrm{1}\:\left(\mathrm{mod}\:\mathrm{4}\right)}\\{\mathrm{4x}=\mathrm{3}\:\left(\mathrm{mod}\:\mathrm{5}\right)\:}\\{\mathrm{5x}=\mathrm{7}\:\left(\mathrm{mod}\:\mathrm{11}\right)}\end{cases} \\ $$ Answered by floor(10²Eta[1]) last updated on 03/Jan/21 $$\mathrm{3x}\equiv\mathrm{1}\left(\mathrm{mod}\:\mathrm{4}\right)\Rightarrow\mathrm{x}\equiv\mathrm{3}\left(\mathrm{mod}\:\mathrm{4}\right) \\ $$$$\mathrm{x}=\mathrm{4a}+\mathrm{3} \\ $$$$\mathrm{4}\left(\mathrm{4a}+\mathrm{3}\right)\equiv\mathrm{3}\left(\mathrm{mod}\:\mathrm{5}\right) \\…
Question Number 62399 by naka3546 last updated on 20/Jun/19 $${What}\:\:{the}\:\:{definition}\:\:{of}\:\:{Claim}\:,\:{Theorem}\:,\:\:{and}\:\:{Lemma}\:\:? \\ $$$${When}\:\:{can}\:\:{we}\:\:{use}\:\:{them}\:\:{respectively}\:\:{for}\:\:{getting}\:\:{proof}\left({s}\right)\:? \\ $$ Answered by alphaprime last updated on 20/Jun/19 $${Lemma}\:−\:{A}\:{proven}\:{statement}\:{used}\:{for}\: \\ $$$${proving}\:{another}\:{statement}\:.\:{It}\:{maybe}\:{like} \\…
Question Number 127933 by AgnibhoMukhopadhyay last updated on 03/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{\frac{\mathrm{1}}{{x}\:−\:\mathrm{3}}\:+\:\frac{\mathrm{1}}{{x}\:+\:\mathrm{4}}} \\ $$$$ \\ $$$$\mathrm{If}\:{x}\:>\:\mathrm{0}\:\mathrm{and}\:{x}\:\neq\:\mathrm{3},\:\mathrm{which}\:\mathrm{of}\:\mathrm{the}\:\:\: \\ $$$$\mathrm{following}\:\mathrm{is}\:\mathrm{equivalent}\:\mathrm{to}\:\mathrm{the}\: \\ $$$$\mathrm{expresion}\:\mathrm{above}? \\ $$$$\mathrm{A}.\:\:\mathrm{2}{x}\:+\:\mathrm{1} \\ $$$$\mathrm{B}.\:\:{x}^{\mathrm{2}} \:+\:{x}\:−\:\mathrm{12}\: \\ $$$$\mathrm{C}.\:\:\frac{{x}^{\mathrm{2}}…