Question Number 80300 by john santu last updated on 02/Feb/20 Commented by ~blr237~ last updated on 02/Feb/20 $$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\:\frac{\mathrm{1}}{{x}}=\mathrm{0}^{−\:\:} \:\:{and}\:\underset{{x}\rightarrow\mathrm{0}^{−} } {\mathrm{lim}}\:\:\frac{\mathrm{1}}{{x}}=−\infty\:\: \\ $$$$\left.\underset{{x}\rightarrow\mathrm{0}^{−} }…
Question Number 145828 by ArielVyny last updated on 08/Jul/21 $$\int\frac{\mathrm{1}}{{x}^{\alpha} +{a}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 145827 by qaz last updated on 08/Jul/21 $$\mathrm{Use}\:\mathrm{Abel}\:\mathrm{summation}\:\mathrm{to}\:\mathrm{evaluate}\::: \\ $$$$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{2n}−\mathrm{1}\right)\centerdot\mathrm{2}^{\mathrm{n}} }=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\mathrm{ln}\left(\sqrt{\mathrm{2}}+\mathrm{1}\right) \\ $$ Answered by Ar Brandon last updated on 08/Jul/21…
Question Number 145777 by Engr_Jidda last updated on 08/Jul/21 $$\int\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}−\mathrm{9}{x}^{\mathrm{2}} }}{dx} \\ $$ Answered by ArielVyny last updated on 08/Jul/21 $$\int\frac{\sqrt{\mathrm{1}−\mathrm{9}{x}^{\mathrm{2}} }}{\mathrm{1}−\mathrm{9}{x}^{\mathrm{2}} }{dx}=\int\frac{\sqrt{\mathrm{1}−\mathrm{9}{x}^{\mathrm{2}} }}{\left(\mathrm{1}−\mathrm{3}{x}\right)\left(\mathrm{1}+\mathrm{3}{x}\right)}{dx} \\…
Question Number 145779 by Engr_Jidda last updated on 08/Jul/21 $${li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\int_{\mathrm{0}} ^{\mathrm{1}} \left({e}^{{t}} +{e}^{−{t}} −\mathrm{2}\right)\frac{{dt}}{\mathrm{1}−{cosx}} \\ $$ Answered by ArielVyny last updated on 08/Jul/21 $${e}^{{t}}…
Question Number 145776 by Engr_Jidda last updated on 08/Jul/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {e}^{{x}} {cosxdx} \\ $$ Answered by ArielVyny last updated on 08/Jul/21 $${I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {e}^{{x}}…
Question Number 145775 by Engr_Jidda last updated on 08/Jul/21 $$\int\frac{\mathrm{2}{x}+\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{5}}}{dx} \\ $$ Answered by mathmax by abdo last updated on 08/Jul/21 $$\Upsilon=\int\:\:\frac{\mathrm{2x}+\mathrm{4}−\mathrm{3}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} \:+\mathrm{4x}+\mathrm{5}}}\mathrm{dx}\:=\int\:\:\frac{\mathrm{2x}+\mathrm{4}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} \:+\mathrm{4x}+\mathrm{5}}}\mathrm{dx}−\mathrm{3}\int\:\frac{\mathrm{dx}}{\:\sqrt{\mathrm{x}^{\mathrm{2}}…
Question Number 80227 by jagoll last updated on 01/Feb/20 $${how}\:{to}\:{prove} \\ $$$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:{x}^{{n}} \:\left(\mathrm{1}−{x}\right)^{{m}\:} \:{dx}\:=\:\frac{{m}!\:×{n}!}{\left({m}+{n}\right)!} \\ $$$${via}\:{Gamma}\:{function} \\ $$ Commented by john santu last…
Question Number 14688 by tawa tawa last updated on 03/Jun/17 $$\int\:\frac{\mathrm{1}}{\mathrm{sin}^{\mathrm{2}} \left(\mathrm{x}\right)\:\mathrm{cos}^{\mathrm{2}} \left(\mathrm{x}\right)}\:\mathrm{dx} \\ $$ Answered by ajfour last updated on 03/Jun/17 $$\int\frac{\mathrm{4}}{\left(\mathrm{2sin}\:{x}\mathrm{cos}\:{x}\right)^{\mathrm{2}} }{dx}\:\:=\mathrm{4}\int\frac{{dx}}{\left(\mathrm{sin}\:\mathrm{2}{x}\right)^{\mathrm{2}} }…
Question Number 145745 by mathmax by abdo last updated on 07/Jul/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{cos}\left(\mathrm{2x}\right)}{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{4}\right)}\mathrm{dx} \\ $$ Answered by mathmax by abdo last…