Category: Integration

Question Number 96034 by  M±th+et+s last updated on 29/May/20 $${\int }_0^{\mathrm{\infty }}\frac{1}{x^{10}+1}dx=\frac{2\pi }{5(\sqrt{5}-1)}=\frac{\pi \varphi }{5}$$ Commented by  M±th+et+s last updated on 30/May/20 $$thanksforsolutions$$…

Question Number 30498 by abdo imad last updated on 22/Feb/18 $$findI={\int }_0^{\sqrt{3}}arcsin\left(\frac{2x}{1+x^2}\right)dx.$$ Answered by sma3l2996 last updated on 24/Feb/18 $${by}\:{part}\:\: \…

Question Number 30494 by abdo imad last updated on 22/Feb/18 $$findI={\int }_0^1\frac{dx}{(1+x)\sqrt{1+x^2}}.$$ Answered by sma3l2996 last updated on 24/Feb/18 $${x}={sinh}\left({t}\right)\Rightarrow{dx}={cosh}\left({t}\right){dt}=\sqrt{\mathrm{1}+{sinh}^{\mathrm{2}} {t}}{dt}…

Question Number 30478 by abdo imad last updated on 22/Feb/18 $$letgive{l}_i\left(x\right)={\int }_2^x\frac{dt}{ln\left(t\right)}findaserieequalto{l}_i\left(x\right).$$$$x⩾2.$$ Terms of Service Privacy Policy Contact:…

Question Number 30475 by abdo imad last updated on 22/Feb/18 $$letgive{f}_n\left(x\right)={\int }_{\frac{1}{n}}^n\frac{sin\left(xt\right)}{t}{e}^{-t}dt$$$$1)find{lim}_{n\to \mathrm{\infty }}{f}_n\left(x\right)$$$$\left.\mathrm{2}\right){find}\:{another}\:{form}\:{of}\:{f}_{{n}} \left({x}\right)\:{by}\:{calculating}\:{f}_{{n}} ^{'} \left({x}\right). \…