Category: Integration

Question Number 71801 by mathmax by abdo last updated on 20/Oct/19 $$find{I}_n={\int }_0^1{x}^n\sqrt{1+x^2}dxwithnintegrnatural$$ Terms of Service Privacy Policy Contact:…

Question Number 71799 by mind is power last updated on 20/Oct/19 Answered by mind is power last updated on 20/Oct/19 $$\mathrm{posted}\mathrm{Quation}\mathrm{two}\mathrm{weeks}\mathrm{Ago}-\mathrm{nice}\mathrm{one}$$ Answered by…

Question Number 6246 by FilupSmith last updated on 20/Jun/16 $$\mathrm{Need}\mathrm{help}\mathrm{solving}{\int }_0^{\mathrm{\infty }}{x}^{-x}dx$$$$\mathrm{My}\mathrm{current}\mathrm{working}:$$$$x^{-x}=e^{-x\ln x}$$$${e}^{−{x}\mathrm{ln}{x}} =\mathrm{1}−{x}\mathrm{ln}\left({x}\right)+\frac{{x}^{\mathrm{2}} \mathrm{ln}\left({x}\right)^{\mathrm{2}} }{\mathrm{2}!}−\frac{{x}^{\mathrm{3}} \mathrm{ln}\left({x}\right)^{\mathrm{3}} }{\mathrm{3}!}+……

Question Number 137307 by mnjuly1970 last updated on 31/Mar/21 $$\dots ..advancedcalculus\dots ..$$$$provethat::$$$$\underset{n=0}{\sum ^{\mathrm{\infty }}}\left(\frac{{(-1)}^n}{4n^2+1}\right)=\frac{1}{4}(2+\pi csch\left(\frac{\pi }{2}\right))$$$$\dots \dots \dots \dots \dots \dots \dots \dots \dots .$$ Answered by Dwaipayan…

Question Number 6220 by sanusihammed last updated on 18/Jun/16 $$\int \sqrt{tanx}dx$$ Answered by malwaan last updated on 19/Jun/16 $$\int \sqrt{tanx}dx=\frac{1}{2\sqrt{2}}(2{tan}^{-1}(1+\sqrt{2tanx})$$$$−\mathrm{2}{tan}^{−\mathrm{1}} \left(\mathrm{1}−\sqrt{\mathrm{2}{tanx}}\right) \…