Question Number 77552 by lémùst last updated on 07/Jan/20 $$\int\frac{\mathrm{x}−\mathrm{2}}{\mathrm{x}^{\mathrm{2}} −{x}+\mathrm{1}}{dx}\:=\:? \\ $$ Answered by MJS last updated on 07/Jan/20 $$\int\frac{{x}−\mathrm{2}}{{x}^{\mathrm{2}} −{x}+\mathrm{1}}{dx}=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{2}{x}−\mathrm{4}}{{x}^{\mathrm{2}} −{x}+\mathrm{1}}{dx}= \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{2}{x}−\mathrm{1}}{{x}^{\mathrm{2}}…
Question Number 12017 by Nayon last updated on 09/Apr/17 $${How}\:{Can}\:{we}\:{expand}\:\left({a}+{b}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \:{and} \\ $$$$\left({a}+{b}\right)^{−{n}} \:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 143090 by mathdave last updated on 10/Jun/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 143085 by Dwaipayan Shikari last updated on 09/Jun/21 $$\phi\left({n}^{\mathrm{4}} +\mathrm{1}\right)=\mathrm{8}{n}\:\:\:\:\:\:\phi:{Euler}\:{totient}\:{function} \\ $$$${Solve}\:{for}\:{n}\in\mathbb{N} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 12015 by Nayon last updated on 09/Apr/17 $${prove}\:{that}\:{for}\:{all}\:{x}\:\in{R}, \\ $$$${e}^{{x}} \geqslant{x}^{{e}} \\ $$ Answered by mrW1 last updated on 18/Apr/17 $${at}\:{x}={e},\:{e}^{{x}} ={x}^{{e}} \\…
Question Number 143087 by bramlexs22 last updated on 10/Jun/21 Answered by Ar Brandon last updated on 10/Jun/21 $$\mathrm{x}=\mathrm{sec}\vartheta \\ $$$$\mathrm{I}=\int_{\frac{\mathrm{2}\pi}{\mathrm{3}}} ^{\frac{\mathrm{5}\pi}{\mathrm{6}}} \frac{\mathrm{sec}\vartheta\mathrm{tan}\vartheta}{\mathrm{sec}\vartheta\sqrt{\mathrm{sec}^{\mathrm{2}} \vartheta−\mathrm{1}}}\mathrm{d}\vartheta=\int_{\frac{\mathrm{2}\pi}{\mathrm{3}}} ^{\frac{\mathrm{5}\pi}{\mathrm{6}}} \frac{\mathrm{tan}\vartheta}{\:\sqrt{\mathrm{tan}^{\mathrm{2}}…
Question Number 12013 by tawa last updated on 09/Apr/17 $$\mathrm{The}\:\mathrm{slope}\:\mathrm{of}\:\mathrm{a}\:\mathrm{curve}\:\mathrm{is},\:\mathrm{7x}\:+\:\mathrm{3}\:\:\mathrm{and}\:\mathrm{it}\:\mathrm{passes}\:\mathrm{through}\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{2},\:\mathrm{4}\right), \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{point} \\ $$ Answered by ajfour last updated on 09/Apr/17 $$\frac{{dy}}{{dx}}=\mathrm{7}{x}+\mathrm{3} \\ $$$$\int{dy}=\int\left(\mathrm{7}{x}+\mathrm{3}\right){dx} \\…
Question Number 143086 by mnjuly1970 last updated on 09/Jun/21 $$ \\ $$$$\:\:{Evaluate}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\Omega:=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \frac{{ln}\left({tan}\left({x}\right)\right).{sin}^{\pi^{{e}} } \left(\mathrm{2}{x}\right)}{\left({sin}^{\pi^{{e}} } \left({x}\right)+{cos}^{\pi^{{e}} } \left({x}\right)\right)^{\mathrm{2}} }{dx} \\ $$$$…
Question Number 77549 by BK last updated on 07/Jan/20 Commented by abdomathmax last updated on 08/Jan/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{dz}}{\mathrm{1}−{xyz}}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \left(\sum_{{n}=\mathrm{0}} ^{\infty} {x}^{{n}} {y}^{{n}} \:{z}^{{n}}…
Question Number 143081 by Mathspace last updated on 09/Jun/21 $${calculate}\:\int_{\mathrm{0}} ^{\infty} {xe}^{−{x}^{\mathrm{2}} } {arctanx}\:{dx} \\ $$ Answered by qaz last updated on 10/Jun/21 $$\int_{\mathrm{0}} ^{\infty}…