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Category: Integration

sec-x-sec-x-tan-x-dx-

Question Number 93005 by i jagooll last updated on 10/May/20 $$\int\:\mathrm{sec}\:\mathrm{x}\:\sqrt{\mathrm{sec}\:\mathrm{x}+\mathrm{tan}\:\mathrm{x}}\:\mathrm{dx}\:=\: \\ $$ Answered by john santu last updated on 10/May/20 $$\int\:\mathrm{sec}\:\mathrm{x}\:\sqrt{\mathrm{sec}\:\mathrm{x}+\mathrm{tan}\:\mathrm{x}}\:\mathrm{dx}\: \\ $$$$\mathrm{set}\:\sqrt{\mathrm{sec}\:\mathrm{x}+\mathrm{tan}\:\mathrm{x}}\:=\:\mathrm{r}\: \\…

Show-that-0-2pi-cos-3x-5-4cos-x-dx-pi-12-

Question Number 27464 by tawa tawa last updated on 07/Jan/18 $$\mathrm{Show}\:\mathrm{that}:\:\:\:\:\int_{\:\mathrm{0}} ^{\:\mathrm{2}\pi} \:\frac{\mathrm{cos}\left(\mathrm{3x}\right)}{\mathrm{5}\:−\:\mathrm{4cos}\left(\mathrm{x}\right)}\:\mathrm{dx}\:\:=\:\:\frac{\pi}{\mathrm{12}} \\ $$ Commented by abdo imad last updated on 07/Jan/18 $${let}\:{put}\:{I}=\:\int_{\mathrm{0}} ^{\mathrm{2}\pi}…

1-decompose-F-x-1-x-4-x-3-5-2-calculate-5-dx-x-4-x-3-5-

Question Number 92971 by abdomathmax last updated on 10/May/20 $$\left.\mathrm{1}\right)\:{decompose}\:{F}\left({x}\right)\:=\frac{\mathrm{1}}{{x}^{\mathrm{4}} \left({x}−\mathrm{3}\right)^{\mathrm{5}} } \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{5}} ^{+\infty} \:\frac{{dx}}{{x}^{\mathrm{4}} \left({x}−\mathrm{3}\right)^{\mathrm{5}} } \\ $$ Commented by mathmax by abdo…

sin-2-x-dx-1-cos-x-2-

Question Number 92960 by i jagooll last updated on 10/May/20 $$\int\:\frac{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}\:\mathrm{dx}}{\left(\mathrm{1}+\mathrm{cos}\:\mathrm{x}\right)^{\mathrm{2}} }\: \\ $$ Answered by i jagooll last updated on 10/May/20 $$\frac{\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}}{\left(\mathrm{1}+\mathrm{cos}\:\mathrm{x}\right)^{\mathrm{2}}…

dx-1-x-7-

Question Number 158492 by bobhans last updated on 05/Nov/21 $$\:\int\:\frac{\mathrm{dx}}{\mathrm{1}+\mathrm{x}^{\mathrm{7}} }\:? \\ $$ Answered by Ar Brandon last updated on 05/Nov/21 $${x}^{\mathrm{7}} +\mathrm{1}=\mathrm{0}\Rightarrow{x}^{\mathrm{7}} ={e}^{\left(\mathrm{2}{k}+\mathrm{1}\right){i}\pi} \Rightarrow{x}_{{k}}…

1-x-sin-1-x-dx-

Question Number 92949 by Ar Brandon last updated on 09/May/20 $$\int\frac{\mathrm{1}}{\mathrm{x}}\mathrm{sin}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)\:\mathrm{dx} \\ $$ Commented by mathmax by abdo last updated on 10/May/20 $${I}\:=\int\:\frac{\mathrm{1}}{{x}}{sin}\left(\frac{\mathrm{1}}{{x}}\right){dx}\:\:{changement}\:\frac{\mathrm{1}}{{x}}={t}\:{give} \\ $$$${I}\:=\int{t}\:{sint}\:\left(−\frac{{dt}}{{t}^{\mathrm{2}}…