Category: Integration

Question Number 199921 by Mingma last updated on 11/Nov/23 Answered by des_ last updated on 12/Nov/23 $${\int }_0^{\mathrm{\infty }}\frac{\cos x}{x^2+1}dx=I;$$$${I}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{cos}\left({ax}\right)}{{x}^{\mathrm{2}} +\mathrm{1}}\:{dx},\:{a}\:>\mathrm{0};…

Question Number 199903 by frankpenredpen last updated on 11/Nov/23 $$\int \frac{x^{2}dx}{\sqrt{x^2-16}}=?$$ Commented by cortano12 last updated on 11/Nov/23 $$\mathrm{why}\partial \mathrm{x}?$$ Answered…

Question Number 199570 by universe last updated on 05/Nov/23 $$\mathrm{I}={\int }_0^{\pi /2}{\tan }^{-1}\left(\frac{\sin x}{2}\right)dx$$ Answered by witcher3 last updated on 05/Nov/23 $$\mathrm{I}\left(\mathrm{a}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{tan}^{−\mathrm{1}}…

Question Number 199468 by Calculusboy last updated on 04/Nov/23 Answered by witcher3 last updated on 04/Nov/23 $$\frac{\mathrm{x}}{2021\pi }\iff$$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\mathrm{e}^{\mathrm{t}^{\mathrm{2021}} } }\left(\mathrm{1}+\mathrm{t}^{\mathrm{2022}} \right)^{\frac{\mathrm{1}}{\mathrm{2022}}} \mathrm{dt}=\mathrm{I}…

Question Number 199377 by universe last updated on 02/Nov/23 $$\int \underset{\mathrm{R}}{\int }\cos \left(\max \{{\mathrm{x}}^3,{\mathrm{y}}^{3/2}\}\right)\mathrm{dx}\mathrm{dy},\mathrm{where}\mathrm{R}=[0,1]\times [0,1]$$ Answered by witcher3 last updated on 04/Nov/23 $$\mathrm{i}\mathrm{will}\mathrm{Try}$$…