Category: Integration

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}}}…

Question Number 40397 by rahul 19 last updated on 21/Jul/18 $$\mathrm{Solve}:$$$$\frac{\mathrm{dy}}{dx}=\frac{\sin y+x}{\sin 2y-x\cos y}.$$ Answered by ajfour last updated on 21/Jul/18 $$\cos y\left(\frac{dy}{dx}\right)=\frac{x+\sin y}{2\sin y-x}$$$${let}\:\:\mathrm{sin}\:{y}={t}…

Question Number 40380 by rahul 19 last updated on 21/Jul/18 $$S\mathrm{olve}:\frac{\mathrm{dy}}{\mathrm{d}x}=\frac{x+y}{x-y}$$ Commented by rahul 19 last updated on 21/Jul/18 $${\mathrm{i}}^{\prime }\mathrm{m}\mathrm{getting}$$$$\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{y}}{{x}}\:=\:{lnx}\:+\:\frac{\mathrm{1}}{\mathrm{2}}{ln}\left(\mathrm{1}+\frac{{y}^{\mathrm{2}}…

Question Number 171392 by cortano1 last updated on 14/Jun/22 $$\underset{0}{\stackrel{\frac{\pi }{2}}{\int }}\frac{\cos x}{{(1+\sqrt{\sin 2x})}^3}dx=?$$ Commented by infinityaction last updated on 19/Jun/22 $$\:\:\:\:\:\:\:{I}\:=\:\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \frac{\mathrm{cos}\:\left(\pi/\mathrm{2}\:−\:{x}\right)}{\mathrm{1}+\sqrt{\mathrm{sin}\:\mathrm{2}\left(\pi/\mathrm{2}\:−{x}\right)}}{dx}…