Question Number 120774 by mnjuly1970 last updated on 02/Nov/20 $$\:\:\:\:\:\:\:\:\:\:…{advanced}\:\:{calculus}… \\ $$$$\:\:\:\:\:\:\:{prove}\:\:{that}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left({x}\right)}{\:\sqrt[{\mathrm{3}}]{\mathrm{1}−{x}^{\mathrm{3}} }}{dx}\overset{???} {=}−\frac{\pi}{\mathrm{3}\sqrt{\mathrm{3}}}\left({ln}\left(\mathrm{3}\right)+\frac{\pi}{\mathrm{3}\sqrt{\mathrm{3}}}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{m}.{n}.\mathrm{1970}… \\ $$ Answered by mindispower…
Question Number 55237 by peter frank last updated on 19/Feb/19 $$\int_{\mathrm{0}} ^{\mathrm{3}} \int_{\mathrm{1}} ^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{2}} \right)\mathrm{dxdy} \\ $$ Commented by Abdo msup. last updated…
Question Number 120775 by mnjuly1970 last updated on 02/Nov/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{advanced}\:\:{calculus}… \\ $$$$\:\:\:\:{evaluate}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Phi\overset{???} {=}\int_{\mathrm{0}} ^{\:\mathrm{1}} {ln}\left({x}\right){tan}^{−\mathrm{1}} \left({x}\right){dx} \\ $$$$\:\:\:\:\:\:\:\:\:…{m}.{n}.\mathrm{1970}… \\ $$ Answered by Dwaipayan…
Question Number 186310 by normans last updated on 03/Feb/23 $$ \\ $$$$\:\:\:\frac{\int\boldsymbol{{x}}\left(\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{5}\right)^{\mathrm{1}/\mathrm{2}} \boldsymbol{{dx}}\:−\:\mathrm{3}\int\boldsymbol{{x}}\left(\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{5}\right)^{−\mathrm{1}/\mathrm{2}} \:\boldsymbol{{dx}}}{\int\:\:\frac{\boldsymbol{{x}}\left[\left(\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{5}\right)−\mathrm{3}\right]}{\:\sqrt{\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{5}\:\:}}\:\boldsymbol{{dx}}}\:=??\:\:\:\: \\ $$$$ \\ $$ Answered by Frix…
Question Number 186306 by MikeH last updated on 03/Feb/23 $$\mathrm{Evaluate}\:\int\frac{\mathrm{ln}\left(\mathrm{sin}\:{x}\right)}{\mathrm{ln}\left(\mathrm{tan}\:{x}\right)+\mathrm{1}}\:{dx} \\ $$ Commented by MJS_new last updated on 03/Feb/23 $$\mathrm{indefinite}\:\mathrm{integral}\:\mathrm{not}\:\mathrm{possible} \\ $$ Commented by normans…
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}}…