Category: Integration

Question Number 43191 by MASANJA J last updated on 08/Sep/18 $$integratebyuseapartialfriction$$$$\int \frac{lnx}{{(1+x)}^2}$$ Commented by mondodotto@gmail.com last updated on 09/Sep/18 $$\mathrm{did}\:\mathrm{you}\:\mathrm{mean}\:\mathrm{by}\:\mathrm{parts}? \…

Question Number 108723 by 150505R last updated on 18/Aug/20 Commented by bemath last updated on 19/Aug/20 $$I=\underset{0}{\stackrel{\pi /2}{\int }}\ln \left(\sqrt{2}\cos (x-\frac{\pi }{4})\right)dx$$$$\:=\:\left[\:{x}\:\mathrm{ln}\:\left(\sqrt{\mathrm{2}}\right)\:\right]_{\mathrm{0}} ^{\pi/\mathrm{2}} +\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\mathrm{ln}\:\left(\mathrm{cos}\:\:\left({x}−\frac{\pi}{\mathrm{4}}\right)\right){dx}…

Question Number 43170 by maxmathsup by imad last updated on 07/Sep/18 $$let{A}_n={\int }_0^{\mathrm{\infty }}\left[n{e}^{-x}\right]dxwithnintegrnatural.$$$$1)calculate{A}_n$$$$2)find{lim}_{n\to +\mathrm{\infty }}{A}_n.$$ Commented…

Question Number 43158 by MASANJA J last updated on 07/Sep/18 $$\int cosecxdx$$ Commented by maxmathsup by imad last updated on 07/Sep/18 $$letI=\int \frac{dx}{sin\left(x\right)}changementtan\left(\frac{x}{2}\right)=tgive$$$${I}\:=\:\int\:\:\:\:\frac{\mathrm{1}}{\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}}…

Question Number 108692 by 150505R last updated on 18/Aug/20 Answered by Dwaipayan Shikari last updated on 18/Aug/20 $${\int }_0^{\frac{\pi }{2}}\frac{2log\left(tan\theta \right)}{{tan}^2\theta +1}{sec}^2\theta d\theta (x=tan\theta ,1={sec}^2\theta \frac{d\theta }{dx})$$$$\mathrm{2}\int_{\mathrm{0}}…