Category: Integration

Question Number 138801 by mnjuly1970 last updated on 18/Apr/21 $$$$$${lim}_{n\to \mathrm{\infty }}\left({\int }_0^1\frac{{(1-x)}^n{e}^x}{n!}dx\right)=?$$ Answered by Kamel last updated on…

Question Number 73258 by Lontum Hans last updated on 09/Nov/19 Answered by MJS last updated on 09/Nov/19 $$\mathrm{well},\mathrm{just}\mathrm{do}\mathrm{it}$$$$u=1+\cosh x\to dx=\frac{du}{\sinh x}$$$$…=\underset{\mathrm{2}} {\overset{\mathrm{3}} {\int}}\frac{{du}}{{u}\left({u}−\mathrm{1}\right)}=\left[\mathrm{ln}\:\frac{{u}−\mathrm{1}}{{u}}\right]_{\mathrm{2}} ^{\mathrm{3}}…

Question Number 138771 by qaz last updated on 18/Apr/21 $${\int }_0^{\pi /2}ln(1-\tan {}^{2}x+\tan {}^{4}x)dx=?$$ Answered by Kamel last updated on 19/Apr/21 Answered by…

Question Number 73231 by mathmax by abdo last updated on 08/Nov/19 $$findthesumof\sum _{n=0}^{\mathrm{\infty }}(n^2-3n+1)e^{-n}$$ Commented by mathmax by abdo last updated on…

Question Number 138742 by mnjuly1970 last updated on 17/Apr/21 $$\dots \dots ..nice\dots .calculus\dots$$$$evaluate::$$$$\mathrm{\Omega }={\int }_0^1\frac{x^{e^{\pi }-1}-x^{e^{\gamma }-1}}{ln\left(\sqrt[3]{x}\right)}dx\stackrel{?}{=}3(\pi -\gamma )$$ Answered by…