Category: Integration

Question Number 149673 by mnjuly1970 last updated on 06/Aug/21 $$\mathrm{solve}::$$$$\left[1\right]\mathit{\varphi }:={\int }_0^{\mathrm{\infty }}\frac{{ln}^2\left(ex\right)}{e^4+x^2}dx=\frac{\pi k}{e^2}$$$$k:=?$$$$$$$$\:\:\:\:\left[\:\mathrm{2}\:\right]\:\:\:\Omega\::=\:\int_{\mathrm{0}\:} ^{\:\infty}…

Question Number 18590 by Joel577 last updated on 25/Jul/17 $$\int \frac{\sin x}{1+{\cos }^{2}x}dx$$ Answered by Arnab Maiti last updated on 25/Jul/17 $$\mathrm{put}\cos \mathrm{x}=\mathrm{z}$$$$\:\:\:\:\:−\mathrm{sin}\:\mathrm{x}\:\mathrm{dx}=\mathrm{dz} \…

Question Number 84100 by niroj last updated on 09/Mar/20 $$\mathrm{Find}\mathrm{the}\mathrm{differential}\mathrm{equations}:$$$$\mathrm{x}\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{y}-\sqrt{{\mathrm{x}}^2+{\mathrm{y}}^2}$$ Answered by TANMAY PANACEA last updated on 09/Mar/20 $${xdy}−{ydx}=−\sqrt{{x}^{\mathrm{2}}…

Question Number 149625 by puissant last updated on 06/Aug/21 $$1){\int }_0^{2\pi }\frac{1}{\mathrm{a}+\sin \left(\mathrm{t}\right)}\mathrm{dt},\mathrm{a}>0$$$$2){\int }_{2\pi }^{4\pi }\frac{1}{2+\sin \left(\mathrm{t}\right)}\mathrm{dt}..$$ Answered by ArielVyny last updated on 06/Aug/21…

Question Number 149608 by puissant last updated on 06/Aug/21 $$\dots ..\mathrm{K}=\int \frac{1}{1+{\sin }^2\left(\mathrm{x}\right)}\mathrm{dx}\dots \dots$$ Answered by ArielVyny last updated on 06/Aug/21 $${sin}^{2}x=\frac{1-cos\left(2x\right)}{2}$$$${K}=\int\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}−{cos}\left(\mathrm{2}{x}\right)}{\mathrm{2}}}=\int\frac{\mathrm{1}}{\frac{\mathrm{2}+\mathrm{1}−{cos}\left(\mathrm{2}{x}\right)}{\mathrm{2}}}{dx} \…