Category: Integration

Question Number 30512 by abdo imad last updated on 22/Feb/18 $$findI={\int }_0^1\sqrt{\frac{1-t}{1+t}}dt.$$ Commented by abdo imad last updated on 24/Feb/18 $${the}\:{ch}.{t}={cos}\theta\:{give}\:{I}=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…

Question Number 30508 by abdo imad last updated on 22/Feb/18 $$findI=\int e^{arcsinx}dx.$$ Commented by sma3l2996 last updated on 24/Feb/18 $$I=\int e^{arcsinx}dx$$$${u}={e}^{{arcsinx}}…

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}…