Question Number 55230 by maxmathsup by imad last updated on 19/Feb/19 $${calculate}\:{lim}_{\xi\rightarrow\mathrm{0}} \:\:\:\:\:\int_{\mathrm{1}} ^{\mathrm{1}+\xi} \:\:\:\:\frac{{arctan}\left(\xi{t}\right)}{{t}}\:{dt}\:. \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 55229 by maxmathsup by imad last updated on 19/Feb/19 $${calculate}\:{lim}_{{n}\rightarrow+\infty} \:\int_{\mathrm{0}} ^{{n}} \:\:\frac{{e}^{{nx}} }{\mathrm{1}+{nx}^{\mathrm{2}} }\:{dx}\:\:. \\ $$ Commented by maxmathsup by imad last…
Question Number 120761 by bramlexs22 last updated on 02/Nov/20 $$\:\:\:\:\int\:\mathrm{tan}^{−\mathrm{1}} \left(\sqrt{\frac{\mathrm{1}−\mathrm{x}}{\mathrm{1}+\mathrm{x}}}\:\right)\:\mathrm{dx}\:? \\ $$ Answered by liberty last updated on 02/Nov/20 $$\mathrm{We}\:\mathrm{put}\:\mathrm{x}\:=\:\mathrm{cos}\:\psi\:\Rightarrow\mathrm{dx}\:=\:−\mathrm{sin}\:\psi\:\mathrm{d}\psi \\ $$$$\int\:\mathrm{tan}^{−\mathrm{1}} \:\sqrt{\frac{\mathrm{1}−\mathrm{cos}\:\psi}{\mathrm{1}+\mathrm{cos}\:\psi}}\:\left(−\mathrm{sin}\:\psi\:\mathrm{d}\psi\right)\:= \\…
Question Number 120758 by bramlexs22 last updated on 02/Nov/20 $$\:\int\:\frac{\mathrm{dx}}{{a}\:\mathrm{sin}\:\mathrm{x}\:+\:{b}\:\mathrm{cos}\:\mathrm{x}} \\ $$ Answered by Dwaipayan Shikari last updated on 02/Nov/20 $$\mathrm{2}\int\frac{{dt}}{{a}\left(\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }\right)+{b}\left(\frac{\mathrm{1}−{t}^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{2}} }\right)}.\frac{\mathrm{1}}{\mathrm{1}+{t}^{\mathrm{2}} }\:\:\:\:\:\:\:\:\:\:\:\:\:{tan}\frac{{x}}{\mathrm{2}}={t}…
Question Number 55223 by peter frank last updated on 19/Feb/19 Commented by maxmathsup by imad last updated on 19/Feb/19 $$\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dx}}{{x}^{{x}} }\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}^{−{x}}…
Question Number 55214 by maxmathsup by imad last updated on 19/Feb/19 $${let}\:{U}_{{n}} =\int_{\frac{\mathrm{1}}{{n}}} ^{\mathrm{1}} \sqrt{{x}^{\mathrm{2}} +\frac{\mathrm{3}}{{n}}}{dx}\:\:\:.{calculate}\:{lim}_{{n}\rightarrow+\infty} {U}_{{n}} \\ $$ Commented by maxmathsup by imad last…
Question Number 55197 by MJS last updated on 19/Feb/19 $$\int\frac{{d}\alpha}{\mathrm{1}−\mathrm{sin}^{\mathrm{3}} \:\alpha}=? \\ $$$$\int\frac{{d}\beta}{\mathrm{1}−\mathrm{cos}^{\mathrm{3}} \:\beta}=? \\ $$$$\int\frac{{d}\gamma}{\mathrm{1}−\mathrm{tan}^{\mathrm{3}} \:\gamma}=? \\ $$ Commented by arvinddayama00@gmail.com last updated on…
Question Number 186246 by Rupesh123 last updated on 02/Feb/23 Answered by Frix last updated on 02/Feb/23 $$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\frac{{dx}}{\:\sqrt{\mathrm{sin}\:{x}\:\left(\mathrm{1}+\mathrm{cos}\:{x}\right)}}\overset{{t}=\mathrm{tan}\:\frac{{x}}{\mathrm{2}}} {=} \\ $$$$=\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\frac{{dt}}{\:\sqrt{{t}}}=\mathrm{2}\left[\sqrt{{t}}\right]_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 120703 by bobhans last updated on 02/Nov/20 $$\:\int\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{2}} \:\sqrt{\mathrm{9}+\mathrm{x}^{\mathrm{2}} }}\:? \\ $$ Answered by john santu last updated on 02/Nov/20 $${let}\:{x}\:=\:\mathrm{3tan}\:{r}\:\Rightarrow{dx}=\mathrm{3sec}\:^{\mathrm{2}} {r}\:{dr} \\…
Question Number 120688 by bobhans last updated on 01/Nov/20 $$\:\underset{\mathrm{0}} {\overset{\pi} {\int}}\:\frac{\mathrm{x}\:\mathrm{dx}}{\mathrm{1}+\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}}\: \\ $$$$ \\ $$ Answered by john santu last updated on 02/Nov/20…