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Category: Integration

Question-158973

Question Number 158973 by mnjuly1970 last updated on 11/Nov/21 Answered by qaz last updated on 11/Nov/21 $$\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \frac{\mathrm{x}}{\left(\mathrm{1}+\mathrm{sin}\:\mathrm{x}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$$$=\frac{\pi}{\mathrm{2}}\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \frac{\mathrm{dx}}{\left(\mathrm{1}+\mathrm{cos}\:\mathrm{x}\right)^{\mathrm{2}} }−\int_{\mathrm{0}}…

1-x-x-1-dx-

Question Number 158965 by cortano last updated on 11/Nov/21 $$\:\int\:\frac{\sqrt{\mathrm{1}+{x}}}{\:\sqrt{{x}}\:+\mathrm{1}}\:{dx}\:=? \\ $$ Answered by puissant last updated on 11/Nov/21 $$\Omega=\int\frac{\sqrt{\mathrm{1}+{x}}}{\:\sqrt{{x}}+\mathrm{1}}{dx} \\ $$$${u}=\sqrt{{x}}\:\rightarrow\:{du}=\frac{{dx}}{\mathrm{2}\sqrt{{x}}}\:\rightarrow\:{dx}=\mathrm{2}{udu} \\ $$$$\Rightarrow\:\Omega\:=\:\int\frac{\mathrm{2}{u}\sqrt{{u}^{\mathrm{2}} +\mathrm{1}}}{{u}+\mathrm{1}}{du}\:;\:…

1-x-6-1-x-8-dx-

Question Number 93410 by  M±th+et+s last updated on 12/May/20 $$\int\frac{\mathrm{1}+{x}^{\mathrm{6}} }{\mathrm{1}+{x}^{\mathrm{8}} }{dx} \\ $$ Commented by prakash jain last updated on 13/May/20 $$\mathrm{Were}\:\mathrm{you}\:\mathrm{able}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{this}.\:\mathrm{My}\: \\ $$$$\mathrm{method}\:\mathrm{of}\:\mathrm{solving}\:\mathrm{by}\:\mathrm{partial}…

Question-27853

Question Number 27853 by Poojadarshini94 last updated on 15/Jan/18 Commented by abdo imad last updated on 17/Jan/18 $${let}\:{put}\:{f}\left({x}\right)=\:{ln}\left({x}+\sqrt{\left.{x}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)}\:\:{we}\:{have}\:\right. \\ $$$${f}'\left({x}\right)=^{\:\:} \:\:\frac{\mathrm{1}\:+\frac{\mathrm{2}{x}}{\mathrm{2}\sqrt{{x}^{\mathrm{2}} +{a}^{\mathrm{2}} }}}{{x}+\sqrt{{x}^{\mathrm{2}}…