Category: Integration

Question Number 33069 by abdo imad last updated on 09/Apr/18 $$byusingresidustheoremprovethat$$$${\int }_0^{\mathrm{\infty }}\frac{t^{a-1}}{1+t}dt=\frac{\pi }{sin\left(\pi a\right)}with0<a<1.$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 98594 by bemath last updated on 15/Jun/20 Answered by bobhans last updated on 15/Jun/20 $$\int\:\mathrm{e}^{\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}}} \:\left(\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{1}\right)\:\mathrm{dx}\:=\:\int\:\mathrm{e}^{\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}}} \:\mathrm{x}^{\mathrm{2}} \:\mathrm{dx}\:+\:\int\:\mathrm{2x}\:\mathrm{e}^{\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}}} \:\mathrm{dx}\:+\:\int\:\mathrm{e}^{\frac{\mathrm{x}^{\mathrm{2}}…

Question Number 98588 by mathmax by abdo last updated on 14/Jun/20 $$\mathrm{calculate}{\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}\frac{\mathrm{xsin}\left(\mathrm{x}\right)}{{({\mathrm{x}}^2+\mathrm{x}+1)}^2}\mathrm{dx}$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 164123 by Zaynal last updated on 14/Jan/22 $$\mathrm{very}\mathrm{nice}\mathrm{to}\mathrm{problem}:$$$$\mathit{f}\mathit{i}\mathit{n}\mathit{d}\mathit{i}\mathit{n}\mathit{c}\mathit{l}\mathit{o}\mathit{s}\mathit{e}\mathit{d}\mathit{f}\mathit{o}\mathit{r}\mathit{m};$$$${\int }_0^1\mathit{l}\mathit{o}\mathit{g}(1-{\mathit{x}}^2)\mathit{l}\mathit{o}\mathit{g}{}^{\mathit{n}}(1-\mathit{x})\mathit{d}\mathit{x};$$$$\mathit{n}\in {\mathbb{N}}^{+}$$$${}^{\mathrm{z}.}$$ Terms…

Question Number 33026 by prof Abdo imad last updated on 09/Apr/18 $$calculate{\int }_0^{\mathrm{\infty }}\frac{1+x^4}{1+x^6}dx.$$ Commented by abdo imad last updated on…