Category: Integration

Question Number 171560 by mnjuly1970 last updated on 17/Jun/22 $$$$$$\mathrm{Nice}\mathrm{Integral}$$$$$$$$\mathrm{\Omega }={\int }_0^{\frac{\pi }{4}}\frac{tan\left(x\right)}{({cos}^2\left(x\right)+2{sin}^2\left(x\right))}dx=$$ Commented by infinityaction…

Question Number 40467 by gunawan last updated on 22/Jul/18 $$\int \ln \mid \sqrt{x+1}+\sqrt{x}\mid dx=$$ Commented by maxmathsup by imad last updated on 22/Jul/18 $$letI=\int ln\mid \sqrt{x+1}+\sqrt{x}\mid dxduetox⩾0wehave$$$${I}\:=\:\int\:{ln}\left(\sqrt{{x}+\mathrm{1}}+\sqrt{{x}}\right){dx}\:=_{\sqrt{{x}}={t}} \:\mathrm{2}\:\:\int{ln}\left(\sqrt{\mathrm{1}+{t}^{\mathrm{2}}…

Question Number 105983 by bemath last updated on 02/Aug/20 $$\int \frac{\sin xdx}{6-\sin {}^{2}x}?$$ Commented by bemath last updated on 02/Aug/20 $$\int \frac{\sin x}{6-(1-\cos {}^{2}x)}dx=-\int \frac{d\left(\cos x\right)}{5+\cos {}^{2}x}$$$${let}\:\flat\:=\:\mathrm{cos}\:{x}…

Question Number 105969 by Ar Brandon last updated on 02/Aug/20 $$\int \frac{\mathrm{sinx}+\mathrm{cosx}}{\sqrt{1+\sin 2\mathrm{x}}}\mathrm{dx}$$ Answered by bobhans last updated on 02/Aug/20 $$\int \frac{\sin \mathrm{x}+\cos \mathrm{x}}{\sqrt{{(\sin \mathrm{x}+\cos \mathrm{x})}^2}}\mathrm{dx}=\int \frac{(\sin \mathrm{x}+\cos \mathrm{x})\mathrm{dx}}{\mid \sin \mathrm{x}+\cos \mathrm{x}\mid }$$$$=\:\pm\:\int\:\mathrm{dx}\:=\:\pm\mathrm{x}\:+\:\mathrm{C} \…

Question Number 105951 by Study last updated on 01/Aug/20 Answered by Dwaipayan Shikari last updated on 01/Aug/20 $$\sqrt{\frac{x}{\sqrt{\frac{x}{\frac{x}{}\dots }}}}=p$$$$\sqrt{\frac{x}{p}}=p$$$$p=\sqrt[3]{x}$$$$\int{pdx}=\int{x}^{\frac{\mathrm{1}}{\mathrm{3}}} {dx}=\frac{\mathrm{3}}{\mathrm{4}}{x}^{\frac{\mathrm{4}}{\mathrm{3}}}…