Category: Integration

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}…

Question Number 40322 by rahul 19 last updated on 19/Jul/18 $$\mathrm{Solve}:$$$$\frac{{\mathrm{d}}^2\mathrm{y}}{\mathrm{d}{x}^2}={\left(\frac{dy}{dx}\right)}^2$$ Commented by rahul 19 last updated on 19/Jul/18…

Question Number 171371 by pticantor last updated on 13/Jun/22 $${\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{\mathit{d}\mathit{x}}{1+{\mathit{x}}^4}=?$$ Answered by aleks041103 last updated on 13/Jun/22 $$solveusingcomplexanalysis$$$${we}\:{inregrate}\:{the}\:{complex}\:{function}…