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Category: Integration

sin-6-2x-cos-6-2x-dx-

Question Number 117100 by bemath last updated on 09/Oct/20 $$\int\:\mathrm{sin}\:^{\mathrm{6}} \left(\mathrm{2x}\right)\:\mathrm{cos}\:^{\mathrm{6}} \left(\mathrm{2x}\right)\:\mathrm{dx}\:=? \\ $$ Answered by Dwaipayan Shikari last updated on 09/Oct/20 $$\int\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{6}} }\left({sin}\mathrm{4}{x}\right)^{\mathrm{6}} {dx}…

advanced-calculus-evsluate-I-0-xsin-2x-x-2-4-dx-hint-0-cos-px-x-2-1-dx-pi-2-e-p-p-gt-0-m

Question Number 117088 by mnjuly1970 last updated on 09/Oct/20 $$\:\:\:\:\:\:\:\:\:\:…\:{advanced}\:\:\:{calculus}… \\ $$$$ \\ $$$$\:\:\:\:\:\:\:{evsluate}\::: \\ $$$$\:\: \\ $$$$\:\:\:\:\:\:\:\mathrm{I}=\int_{\mathrm{0}} ^{\:\infty} \frac{{xsin}\left(\mathrm{2}{x}\right)}{{x}^{\mathrm{2}} +\mathrm{4}}\:{dx}\:=? \\ $$$$\:\:\:\:\:{hint}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\Phi=\int_{\mathrm{0}}…

find-f-0-pi-4-1-tant-dt-with-gt-0-also-calculate-0-pi-4-tant-1-tant-dt-

Question Number 51551 by maxmathsup by imad last updated on 28/Dec/18 $${find}\:{f}\left(\lambda\right)\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \sqrt{\mathrm{1}+\lambda{tant}}{dt}\:\:\:{with}\:\lambda>\mathrm{0} \\ $$$${also}\:{calculate}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{tant}}{\:\sqrt{\mathrm{1}+\lambda{tant}}}{dt}. \\ $$ Commented by Abdo msup. last…

Given-f-x-x-1-x-1-If-f-2-x-f-f-x-f-3-x-f-f-f-x-f-1998-x-g-x-then-1-e-1-g-x-dx-

Question Number 117066 by bemath last updated on 09/Oct/20 $$\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}\right)=\:\frac{\mathrm{x}−\mathrm{1}}{\mathrm{x}+\mathrm{1}}\:.\:\mathrm{If}\:\mathrm{f}^{\mathrm{2}} \left(\mathrm{x}\right)=\mathrm{f}\left(\mathrm{f}\left(\mathrm{x}\right)\right),\: \\ $$$$\mathrm{f}^{\mathrm{3}} \left(\mathrm{x}\right)=\mathrm{f}\left(\mathrm{f}\left(\mathrm{f}\left(\mathrm{x}\right)\right)\right)\:,\:\mathrm{f}^{\mathrm{1998}} \left(\mathrm{x}\right)\:=\:\mathrm{g}\left(\mathrm{x}\right) \\ $$$$\mathrm{then}\:\int_{\frac{\mathrm{1}}{\mathrm{e}}} ^{\mathrm{1}} \mathrm{g}\left(\mathrm{x}\right)\:\mathrm{dx}\:=\:\_? \\ $$ Answered by 1549442205PVT last…