Category: Differentiation

Question Number 86092 by ar247 last updated on 27/Mar/20 $$\int \frac{1}{\sqrt{5-4x-2x^2}}dx$$ Commented by abdomathmax last updated on 27/Mar/20 $$I=\int \frac{dx}{\sqrt{-2x^2-4x+5}}wehave$$$${I}=\int\:\:\:\frac{{dx}}{\:\sqrt{\mathrm{5}−\mathrm{2}\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{1}−\mathrm{1}\right)}}=\int\:\:\frac{{dx}}{\:\sqrt{\mathrm{5}−\mathrm{2}\left({x}+\mathrm{1}\right)^{\mathrm{2}}…

Question Number 151175 by alcohol last updated on 18/Aug/21 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 151118 by mnjuly1970 last updated on 18/Aug/21 $$$$$${\int }_0^{\mathrm{\infty }}\frac{arctan\left(\frac{x}{2}\right)+arctan\left(2x\right)}{x^2+1}\stackrel{?}{=}\frac{{\pi }^2}{4}$$$$$$ Answered by Olaf_Thorendsen last…

Question Number 85513 by niroj last updated on 22/Mar/20 $$\mathbf{Solve}\mathbf{the}\mathbf{following}\mathbf{equation}:$$$${\left(\frac{\mathbf{dy}}{\mathbf{dx}}\right)}^2+2\mathbf{y}\mathbf{cot}\mathbf{x}\frac{\mathbf{dy}}{\mathbf{dx}}={\mathbf{y}}^2$$ Answered by mr W last updated on 22/Mar/20 $$\frac{{dy}}{{dx}}=−{y}\:\mathrm{cot}\:{x}\pm\sqrt{{y}^{\mathrm{2}} \mathrm{cot}^{\mathrm{2}}…

Question Number 150963 by EDWIN88 last updated on 17/Aug/21 $$Givenx,yrealnumbersuchthat$$$$0<\frac{y}{x}<\frac{1}{2}.Findminimumvalue$$$$of\frac{2y}{x-y}+\frac{3x}{x+2y}.$$ Answered by john_santu last updated on 17/Aug/21 $$\:\mathrm{let}\:\frac{\mathrm{y}}{\mathrm{x}}\:=\:\mathrm{t}\:\Rightarrow\mathrm{f}\left(\mathrm{t}\right)=\frac{\mathrm{2t}}{\mathrm{1}−\mathrm{t}}+\frac{\mathrm{3}}{\mathrm{1}+\mathrm{2t}}\: \…