Question Number 65675 by mathmax by abdo last updated on 01/Aug/19 $$\left.\mathrm{1}\right)\:{find}\:\int\:\frac{{dx}}{\:\sqrt{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}−\mathrm{2}\right)}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 131211 by mnjuly1970 last updated on 02/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:…{calculus}… \\ $$$$\:{prove}\:{that}:: \\ $$$$\:\boldsymbol{\Phi}=\int_{\mathrm{0}} ^{\:\frac{\boldsymbol{\pi}}{\mathrm{4}}} \left(\frac{\sqrt{\boldsymbol{{tan}}\left(\boldsymbol{{x}}\right)+\boldsymbol{{tan}}^{\mathrm{2}} \left(\boldsymbol{{x}}\right)}}{\:\sqrt{\boldsymbol{{tan}}\left(\boldsymbol{{x}}\right)−\boldsymbol{{tan}}^{\mathrm{2}} \left(\boldsymbol{{x}}\right)}}\:\boldsymbol{{sin}}\left(\boldsymbol{{x}}\right)\right)\boldsymbol{{dx}}\: \\ $$$$\:\:\:\:=\frac{\mathrm{1}}{\mathrm{2}}+\frac{\sqrt{\boldsymbol{\pi}}}{\mathrm{8}}\:\left(\frac{\boldsymbol{\Gamma}\left(\frac{\mathrm{1}}{\mathrm{4}}\right)}{\boldsymbol{\Gamma}\left(\frac{\mathrm{3}}{\mathrm{4}}\right)}−\frac{\boldsymbol{\Gamma}\left(\frac{\mathrm{3}}{\mathrm{4}}\right)}{\boldsymbol{\Gamma}\left(\frac{\mathrm{5}}{\mathrm{4}}\right)}\right) \\ $$ Answered by Ar…
Question Number 137 by novrya last updated on 25/Jan/15 $${Solve}\:\mathrm{2}{x}\:\equiv\:\mathrm{6}\:\left({mod}\:\mathrm{8}\right) \\ $$ Answered by mreddy last updated on 10/Dec/14 $$\mathrm{gcd}\left(\mathrm{2},\mathrm{8}\right)=\mathrm{2},\:\mathrm{2}\:\mathrm{divides}\:\mathrm{6}\: \\ $$$$\mathrm{So}\:\mathrm{there}\:\mathrm{are}\:\mathrm{2}\:\mathrm{distinct}\:\mathrm{solutions} \\ $$$$\mathrm{Solutions}\:\mathrm{for}\:{x}\:\mathrm{are}\:\mathrm{given}\:\mathrm{by}\:\mathrm{equation} \\…
Question Number 65673 by mathmax by abdo last updated on 01/Aug/19 $${find}\:\sum_{{n}=\mathrm{2}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}} }{\left({n}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Commented by mathmax by abdo last…
Question Number 134 by novrya last updated on 25/Jan/15 $${Solve}\:{for}\:\mathrm{3}{x}\equiv\mathrm{4}\:\left({mod}\:\mathrm{5}\right) \\ $$ Answered by rajabhay last updated on 09/Dec/14 $$\mathrm{gcd}\left(\mathrm{3},\mathrm{5}\right)=\mathrm{1}\:\mathrm{and}\:\mathrm{1}\:\mathrm{divides}\:\mathrm{4}\: \\ $$$$\mathrm{There}\:\mathrm{is}\:\mathrm{only}\:\mathrm{solution}\: \\ $$$${x}=\mathrm{3}\:\left({mod}\:\mathrm{5}\right) \\…
Question Number 133 by sagarwal last updated on 25/Jan/15 $$\mathrm{Evaluate}\:\int\sqrt{\mathrm{sin}\:{x}}{dx} \\ $$ Answered by gkfichadia last updated on 10/Dec/14 $$ \\ $$$$ \\ $$$$ \\…
Question Number 131206 by Study last updated on 02/Feb/21 $${f}\left({x}\right)=\infty \\ $$$$\frac{{d}}{{dx}}{f}\left({x}\right)=? \\ $$ Commented by mr W last updated on 02/Feb/21 $$\infty\:{is}\:{not}\:{a}\:{variable},\:{is}\:{not}\:{a}\:{constant}. \\ $$$${f}\left({x}\right)=\infty\:{has}\:{no}\:{meaning}!…
Question Number 131201 by shaker last updated on 02/Feb/21 Answered by liberty last updated on 11/Feb/21 $$\mathrm{L}=\int\:\frac{\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}}{\mathrm{cos}\:\mathrm{2x}}\:\mathrm{dx}\:;\:\mathrm{by}\:\mathrm{change}\:\mathrm{of}\:\mathrm{variable}\: \\ $$$$\:\mathrm{let}\:\mathrm{u}\:=\:\mathrm{tan}\:\mathrm{x}\:\rightarrow\begin{cases}{\mathrm{dx}=\frac{\mathrm{du}}{\mathrm{1}+\mathrm{u}^{\mathrm{2}} }}\\{\mathrm{cos}\:\mathrm{2x}=\frac{\mathrm{1}−\mathrm{u}^{\mathrm{2}} }{\mathrm{1}+\mathrm{u}^{\mathrm{2}} }}\end{cases} \\ $$$$\mathrm{L}=\int\:\left(\frac{\mathrm{u}^{\mathrm{2}}…
Question Number 131 by novrya last updated on 25/Jan/15 $$\int\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{4}} }\:{dx}\:=…. \\ $$$$ \\ $$ Answered by rajabhay last updated on 08/Dec/14 $$\int\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{4}} }{dx}=\int\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{{x}^{\mathrm{2}} +\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{4}}…
Question Number 131200 by aurpeyz last updated on 02/Feb/21 Terms of Service Privacy Policy Contact: info@tinkutara.com