Question Number 32958 by artibunja last updated on 07/Apr/18 Commented by MJS last updated on 07/Apr/18 $$\frac{{x}^{\mathrm{2}} −\mathrm{3}{x}−\mathrm{10}}{\mathrm{3}{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{3}}+\frac{\left(−\mathrm{3}+\frac{\mathrm{5}}{\mathrm{3}}\right){x}+\left(−\mathrm{10}−\frac{\mathrm{2}}{\mathrm{3}}\right)}{\mathrm{3}{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{2}}= \\ $$$$=\frac{\mathrm{1}}{\mathrm{3}}−\frac{\mathrm{4}}{\mathrm{3}}×\frac{{x}+\mathrm{8}}{\mathrm{3}{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{2}} \\ $$$$\mathrm{3}{x}^{\mathrm{2}}…
Question Number 32951 by math1967 last updated on 07/Apr/18 $${Evaluate} \\ $$$$\int\frac{{x}^{\mathrm{4}} +\mathrm{1}}{{x}^{\mathrm{6}} +\mathrm{1}}{dx}\:\:\:\:\:\left[{W}.{B}.{H}.{S}\:\mathrm{2018}\right] \\ $$ Commented by abdo imad last updated on 09/Apr/18 $${yes}\:{i}\:{have}\:{commited}\:{a}\:{error}\:\:{becaus}\:{i}\:{don}\:{t}\:{give}\:…
Question Number 32939 by abdo imad last updated on 06/Apr/18 $$\left.\mathrm{1}\right)\:{study}\:{the}\:{convergence}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{x}^{{p}} }{\mathrm{1}+{x}}\:{dx} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{p}\rightarrow\infty} \:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{x}^{{p}} }{\mathrm{1}+{x}}{dx}\:. \\ $$ Commented by abdo…
Question Number 32928 by Cheyboy last updated on 06/Apr/18 $$\boldsymbol{{plz}}\:\boldsymbol{{help}} \\ $$$${Evalute} \\ $$$$ \\ $$$$\underset{\pi/\mathrm{3}\:} {\overset{\pi/\mathrm{4}} {\int}}\:\frac{\mathrm{sin}^{\mathrm{2}} {x}}{\:\sqrt{\mathrm{1}−{cosx}}}{dx} \\ $$ Commented by abdo imad…
Question Number 98463 by pranesh last updated on 14/Jun/20 Answered by maths mind last updated on 15/Jun/20 $$\underset{{k}=\mathrm{1}} {\overset{\mathrm{99}} {\sum}}\frac{{x}^{{k}} }{{k}}=\int\frac{\mathrm{1}−{x}^{\mathrm{99}} }{\mathrm{1}−{x}}{dx} \\ $$$$\left({cot}\left({x}\right)+……+\frac{{cot}^{\mathrm{99}} \left({x}\right)}{\mathrm{99}}\right)+\int\left(\mathrm{1}+{cot}\left({x}\right)\right)\left(\mathrm{1}+{cot}^{\mathrm{99}}…
Question Number 98444 by mathmax by abdo last updated on 14/Jun/20 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{lnx}}{\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$ Answered by abdomathmax last updated on 14/Jun/20 $$\mathrm{I}\:=\int_{\mathrm{0}}…
Question Number 98445 by mathmax by abdo last updated on 14/Jun/20 $$\mathrm{give}\:\mathrm{at}\:\mathrm{form}\:\mathrm{of}\:\mathrm{serie}\:\mathrm{U}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{x}^{\mathrm{n}} \mathrm{ln}\left(\mathrm{x}\right)}{\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$ Answered by mathmax by abdo last…
Question Number 98428 by mathmax by abdo last updated on 13/Jun/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{2}} \:\:,\mathrm{2}\pi\:\mathrm{periodi}\:\mathrm{even}\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$ Answered by mathmax by abdo last updated on 14/Jun/20 $$\mathrm{f}\:\mathrm{is}\:\mathrm{even}\:\Rightarrow\mathrm{f}\left(\mathrm{x}\right)\:=\frac{\mathrm{a}_{\mathrm{0}}…
Question Number 98426 by mathmax by abdo last updated on 13/Jun/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{3}}} \:\frac{\mathrm{dt}}{\mathrm{x}+\mathrm{tant}}\:\:\mathrm{calculate}\:\mathrm{f}\left(\mathrm{x}\right) \\ $$$$\left.\mathrm{2}\right)\mathrm{explicit}\:\mathrm{g}\left(\mathrm{x}\right)\:=\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{3}}} \:\frac{\mathrm{dt}}{\left(\mathrm{x}+\mathrm{tant}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{integrals}\:\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{3}}} \:\frac{\mathrm{dt}}{\mathrm{2}+\mathrm{tant}}\:\mathrm{and}\:\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{3}}} \:\frac{\mathrm{dt}}{\left(\mathrm{2}+\mathrm{tant}\right)^{\mathrm{2}}…
Question Number 98423 by mathmax by abdo last updated on 13/Jun/20 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }} \mathrm{dx} \\ $$ Answered by maths mind last updated…