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Category: Integration

Question-91990

Question Number 91990 by Power last updated on 04/May/20 Commented by mathmax by abdo last updated on 04/May/20 $${I}\:=\int\:\frac{{x}^{\mathrm{3}} −\mathrm{6}}{{x}^{\mathrm{4}} \:+\mathrm{6}{x}\:+\mathrm{8}}\:\Rightarrow\:{I}\:=\frac{\mathrm{1}}{\mathrm{4}}\int\:\:\frac{\mathrm{4}{x}^{\mathrm{3}} −\mathrm{24}}{{x}^{\mathrm{4}} \:+\mathrm{6}{x}\:+\mathrm{8}}{dx}\:\Rightarrow \\ $$$$\mathrm{4}{I}\:=\int\frac{\mathrm{4}{x}^{\mathrm{3}}…

Question-26446

Question Number 26446 by yesaditya22@gmail.com last updated on 25/Dec/17 Answered by ajfour last updated on 25/Dec/17 $$\mathrm{cos}\:\theta\mathrm{sin}\:\theta+\mathrm{sin}\:\theta\mathrm{cos}\:\theta={a} \\ $$$$\Rightarrow\:\mathrm{sin}\:\mathrm{2}\theta={a} \\ $$$$\frac{{d}\left(\mathrm{sin}\:\theta\right)}{{d}\left(\mathrm{cos}\:\theta\right)}=\frac{\mathrm{cos}\:\theta}{−\mathrm{sin}\:\theta}\:=−\sqrt{\frac{\mathrm{1}−{y}^{\mathrm{2}} }{\mathrm{1}−{x}^{\mathrm{2}} }}\:. \\ $$…

If-f-x-is-an-even-function-is-n-f-n-2-n-0-f-n-true-

Question Number 91960 by frc2crc last updated on 04/May/20 $$\mathrm{If} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{an}\:{e}\mathrm{ven}\:\mathrm{function}\:\mathrm{is} \\ $$$$\underset{{n}=−\infty} {\overset{\infty} {\sum}}{f}\left({n}\right)=\mathrm{2}\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}{f}\left({n}\right)\:{true}? \\ $$ Commented by abdomathmax last updated…

cos-3-2x-sin-3-3x-dx-

Question Number 91961 by jagoll last updated on 04/May/20 $$\int\:\mathrm{cos}\:^{\mathrm{3}} \left(\mathrm{2x}\right)\:\mathrm{sin}\:^{\mathrm{3}} \left(\mathrm{3x}\right)\:\mathrm{dx}\: \\ $$ Commented by mathmax by abdo last updated on 04/May/20 $${cos}\left(\mathrm{2}{x}\right){sin}\left(\mathrm{3}{x}\right)\:={cos}\left(\mathrm{2}{x}\right){cos}\left(\frac{\pi}{\mathrm{2}}−\mathrm{3}{x}\right) \\…