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Category: Integration

6x-4-4-x-4-2-dx-

Question Number 85441 by jagoll last updated on 22/Mar/20 $$\int\:\frac{\mathrm{6x}^{\mathrm{4}} −\mathrm{4}}{\:\sqrt{\mathrm{x}^{\mathrm{4}} −\mathrm{2}}}\:\mathrm{dx}\:=\:? \\ $$ Answered by john santu last updated on 22/Mar/20 $${I}\:=\:\int\:\frac{\mathrm{4}{x}^{\mathrm{4}} }{\:\sqrt{{x}^{\mathrm{4}} −\mathrm{2}}}\:{dx}\:=\:\mathrm{4}\int\:{x}\:\left(\frac{{x}^{\mathrm{3}}…

pi-4-0-sin-x-cos-x-9-16sin-2x-dx-

Question Number 85426 by john santu last updated on 22/Mar/20 $$\int\:_{\frac{\pi}{\mathrm{4}}} ^{\mathrm{0}} \:\frac{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{\mathrm{9}+\mathrm{16sin}\:\mathrm{2}{x}}\:{dx} \\ $$ Commented by som(math1967) last updated on 22/Mar/20 $$\int\frac{{sinx}+{cosx}}{\mathrm{25}−\mathrm{16}\left(\mathrm{1}−{sin}\mathrm{2}{x}\right)}{dx} \\ $$$$\frac{\mathrm{1}}{\mathrm{4}}\int\frac{\mathrm{4}\left({sinx}+{cosx}\right)}{\mathrm{5}^{\mathrm{2}}…

1-1-cos-x-dx-

Question Number 85414 by M±th+et£s last updated on 21/Mar/20 $$\int\frac{\mathrm{1}}{\mathrm{1}+\sqrt{{cos}\left({x}\right)}\:}\:{dx} \\ $$ Commented by M±th+et£s last updated on 21/Mar/20 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{1}}{\mathrm{1}+\sqrt{{cos}\left({x}\right)}}\:{dx}\:\:\:{typo}….\: \\ $$ Answered…

I-cosx-2sinx-e-2x-sinx-dx-

Question Number 150932 by maged last updated on 16/Aug/21 $$\mathrm{I}=\int\frac{\mathrm{cosx}\:−\:\mathrm{2sinx}}{\mathrm{e}^{\mathrm{2x}} −\mathrm{sinx}}\mathrm{dx}\overset{?} {=} \\ $$ Answered by Olaf_Thorendsen last updated on 16/Aug/21 $$\mathrm{F}\left({x}\right)\:=\:\int\frac{\mathrm{cos}{x}−\mathrm{2sin}{x}}{{e}^{\mathrm{2}{x}} −\mathrm{sin}{x}}\:{dx} \\ $$$$\mathrm{F}\left({x}\right)\:=\:\int\frac{\left(\mathrm{2}{e}^{\mathrm{2}{x}}…