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Category: Integration

Question-161773

Question Number 161773 by smallEinstein last updated on 22/Dec/21 Commented by Tawa11 last updated on 22/Dec/21 $$\mathrm{Sir}\:\mathrm{einstein},\:\mathrm{please}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{name}\:\mathrm{of}\:\mathrm{this}\:\mathrm{app}? \\ $$ Answered by Ar Brandon last updated…

calculate-f-a-0-cos-sh-2x-x-2-a-2-dx-and-g-a-0-cos-sh-2x-x-2-a-2-2-a-gt-0-

Question Number 96198 by mathmax by abdo last updated on 30/May/20 $$\mathrm{calculate}\:\mathrm{f}\left(\mathrm{a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{cos}\left(\mathrm{sh}\left(\mathrm{2x}\right)\right)}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{a}^{\mathrm{2}} }\mathrm{dx}\:\mathrm{and}\:\mathrm{g}\left(\mathrm{a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{cos}\left(\mathrm{sh}\left(\mathrm{2x}\right)\right)}{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{a}^{\mathrm{2}} \right)^{\mathrm{2}} }\:\:\:\left(\mathrm{a}>\mathrm{0}\right) \\ $$ Answered by…

dx-4x-2-4x-3-

Question Number 96175 by Fikret last updated on 30/May/20 $$\int\frac{{dx}}{\:\sqrt{\mathrm{4}{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{3}}}=? \\ $$ Commented by bobhans last updated on 30/May/20 $$\int\:\frac{{dx}}{\mathrm{2}\sqrt{{x}^{\mathrm{2}} +{x}+\frac{\mathrm{3}}{\mathrm{4}}}}\:=\:\int\:\frac{{dx}}{\mathrm{2}\sqrt{\left({x}+\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{2}}}} \\ $$$${set}\:{x}+\frac{\mathrm{1}}{\mathrm{2}}\:=\:\sqrt{\frac{\mathrm{1}}{\mathrm{2}}}\:\mathrm{tan}\:{u}\:\Rightarrow\mathrm{tan}\:\mathrm{u}\:=\:\frac{\mathrm{2x}+\mathrm{1}}{\:\sqrt{\mathrm{2}}}…

1-sin-x-cos-x-sin-2x-dx-2-0-pi-2-cos-7x-cos-17x-cos-37x-dx-

Question Number 161703 by cortano last updated on 21/Dec/21 $$\left(\mathrm{1}\right)\int\:\frac{\mathrm{sin}\:{x}−\mathrm{cos}\:{x}}{\:\sqrt{\mathrm{sin}\:\mathrm{2}{x}}}\:{dx} \\ $$$$\left(\mathrm{2}\right)\:\int_{\mathrm{0}} ^{\:\pi/\mathrm{2}} \mathrm{cos}\:\mathrm{7}{x}\:\mathrm{cos}\:\mathrm{17}{x}\:\mathrm{cos}\:\mathrm{37}{x}\:{dx} \\ $$ Commented by cortano last updated on 21/Dec/21 $$\left(\mathrm{1}\right)\:\Omega\:=\int\:\frac{\mathrm{sin}\:{x}−\mathrm{cos}\:{x}}{\:\sqrt{\mathrm{1}+\mathrm{sin}\:\mathrm{2}{x}−\mathrm{1}}}\:{dx} \\…