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Category: Integration

Question-128529

Question Number 128529 by bramlexs22 last updated on 08/Jan/21 Commented by liberty last updated on 08/Jan/21 $$\mathrm{considering}\:\frac{\mathrm{d}}{\mathrm{dx}}\left(\frac{\mathrm{u}}{\mathrm{v}}\right)=\frac{\mathrm{u}'\mathrm{v}−\mathrm{uv}'}{\mathrm{v}^{\mathrm{2}} } \\ $$$$\:\mathrm{obvious}\:\mathrm{v}=\mathrm{2}+\mathrm{3cos}\:\mathrm{x}\:\mathrm{and}\:\mathrm{3}+\mathrm{2cos}\:\mathrm{x}=\mathrm{u}'\left(\mathrm{2}+\mathrm{3cos}\:\mathrm{x}\right)−\mathrm{u}\left(−\mathrm{3sin}\:\mathrm{x}\right) \\ $$$$\Rightarrow\mathrm{2cos}\:\mathrm{x}+\mathrm{3}=\mathrm{2u}'+\mathrm{3u}'\mathrm{cos}\:\mathrm{x}+\mathrm{3u}\:\mathrm{sin}\:\mathrm{x} \\ $$$$\mathrm{check}\:\mathrm{u}\:=\:\mathrm{sin}\:\mathrm{x}\:\Rightarrow\:\mathrm{u}'\left(\mathrm{2}+\mathrm{3cosx}\right)+\mathrm{3u}\:\mathrm{sin}\:\mathrm{x}=\: \\…

Question-62981

Question Number 62981 by hovea cw last updated on 27/Jun/19 Commented by mathmax by abdo last updated on 27/Jun/19 $$\left.\mathrm{2}\right)\:{let}\:{A}\:=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{x}\mid{sin}\left(\mathrm{2}{x}\right)\mid}{\mathrm{3}+{sin}^{\mathrm{2}} {x}}\:{dx}\:{changement}\:{x}\:=\pi\:+{t}\:{give} \\ $$$${A}\:=\int_{−\pi}…