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Category: Integration

0-1-sin-x-cos-2-x-cos-2-pi-5-cos-2-x-cos-2-2pi-5-sin-5x-dx-

Question Number 177906 by cortano1 last updated on 11/Oct/22 $$\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\mathrm{sin}\:\mathrm{x}\left(\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}−\mathrm{cos}\:^{\mathrm{2}} \frac{\pi}{\mathrm{5}}\right)\left(\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}−\mathrm{cos}\:^{\mathrm{2}} \frac{\mathrm{2}\pi}{\mathrm{5}}\right)}{\mathrm{sin}\:\mathrm{5x}}\:\mathrm{dx}\:=? \\ $$ Answered by Frix last updated on 11/Oct/22…

pi-2-pi-dx-sin-x-2cos-x-2-

Question Number 177820 by cortano1 last updated on 09/Oct/22 $$\:\:\:\:\underset{\pi/\mathrm{2}} {\overset{\pi} {\int}}\:\frac{\mathrm{dx}}{\left(\mathrm{sin}\:\mathrm{x}−\mathrm{2cos}\:\mathrm{x}\right)^{\mathrm{2}} }\:=? \\ $$ Answered by qaz last updated on 09/Oct/22 $$\int_{\pi/\mathrm{2}} ^{\pi} \frac{{dx}}{\left(\mathrm{sin}\:{x}−\mathrm{2cos}\:{x}\right)^{\mathrm{2}}…

find-x-1-x-1-x-dx-

Question Number 46740 by math khazana by abdo last updated on 30/Oct/18 $${find}\:\int\:\:{x}\sqrt{\frac{\mathrm{1}−\sqrt{{x}}}{\mathrm{1}+\sqrt{{x}}}}{dx} \\ $$ Commented by behi83417@gmail.com last updated on 31/Oct/18 $$=\int{x}.\sqrt{\frac{\left(\mathrm{1}−\sqrt{{x}}\right)\left(\mathrm{1}−\sqrt{{x}}\right)}{\left(\mathrm{1}+\sqrt{{x}}\right)\left(\mathrm{1}−\sqrt{{x}}\right)}}{dx}= \\ $$$$=\int{x}.\frac{\mathrm{1}−\sqrt{{x}}}{\:\sqrt{\mathrm{1}−{x}}}{dx}=\int\left[\frac{{x}}{\:\sqrt{\mathrm{1}−{x}}}−\frac{{x}\sqrt{{x}}}{\:\sqrt{\mathrm{1}−{x}}}\right]{dx}=…

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

Question Number 112271 by bemath last updated on 07/Sep/20 $$\:\:\:\:\sqrt{\mathrm{bemath}} \\ $$$$\:\:\:\int\:\mathrm{sin}\:\mathrm{x}\:\sqrt{\mathrm{1}−\mathrm{sin}\:\mathrm{x}}\:\mathrm{dx}\:? \\ $$ Answered by maths mind last updated on 07/Sep/20 $$\mathrm{1}−{sin}\left({x}\right)=\left({sin}\left(\frac{{x}}{\mathrm{2}}\right)−{cos}\left(\frac{{x}}{\mathrm{2}}\right)\right)^{\mathrm{2}} \\ $$…

Question-46720

Question Number 46720 by Necxx last updated on 30/Oct/18 Commented by Necxx last updated on 30/Oct/18 $${please}\:{help}\:{with}\:{no}.\:\mathrm{15}\:{cos}\:{i}\:{got}\:{it} \\ $$$${as} \\ $$$$−\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{{x}}\right)−\:\frac{\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}{{x}}\:+{c} \\ $$…

dx-x-4-1-x-2-1-

Question Number 112251 by bobhans last updated on 07/Sep/20 $$\int\:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{4}} −\mathrm{1}\right)\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}} \\ $$ Answered by john santu last updated on 07/Sep/20 $$\int\:\frac{{dx}}{\left({x}^{\mathrm{4}} −\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}\:?…