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Category: Integration

dx-1-x-2-1-x-2-

Question Number 127355 by bemath last updated on 29/Dec/20 $$\:\int\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\:=?\: \\ $$ Answered by liberty last updated on 29/Dec/20 $$\:{I}=\int\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\:;\:\left[\:{x}\:=\:\mathrm{sin}\:{h}\:\right]\: \\…

Question-61809

Question Number 61809 by aliesam last updated on 09/Jun/19 Commented by maxmathsup by imad last updated on 10/Jun/19 $${let}\:{A}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{x}^{{n}} }{\:\sqrt{{ln}\left({x}\right)}}\:{dx}\:\Rightarrow\:{A}\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{x}^{{n}} }{\:\sqrt{−\left(−{lnx}\right)}}\:{dx}\:=\frac{\mathrm{1}}{\:\sqrt{−\mathrm{1}}}\:\int_{\mathrm{0}}…

2pi-4pi-1-cos-x-dx-

Question Number 61801 by aliesam last updated on 08/Jun/19 $$\underset{\mathrm{2}\pi} {\overset{\mathrm{4}\pi} {\int}}\sqrt{\mathrm{1}−{cos}\left({x}\right)}\:{dx} \\ $$ Commented by MJS last updated on 08/Jun/19 $$\sqrt{\mathrm{1}−\mathrm{cos}\:{x}}=\sqrt{\mathrm{2}}\mathrm{sin}\:\frac{{x}}{\mathrm{2}} \\ $$$$\mathrm{now}\:\mathrm{it}'\mathrm{s}\:\mathrm{easy} \\…