Category: Integration

Question Number 120775 by mnjuly1970 last updated on 02/Nov/20 $$\dots advancedcalculus\dots$$$$evaluate::$$$$\mathrm{\Phi }\stackrel{???}{=}{\int }_0^{1}ln\left(x\right){tan}^{-1}\left(x\right)dx$$$$\dots m.n.1970\dots$$ Answered by Dwaipayan…

Question Number 186306 by MikeH last updated on 03/Feb/23 $$\mathrm{Evaluate}\int \frac{\ln \left(\sin x\right)}{\ln \left(\tan x\right)+1}dx$$ Commented by MJS_new last updated on 03/Feb/23 $$\mathrm{indefinite}\mathrm{integral}\mathrm{not}\mathrm{possible}$$ Commented by normans…

Question Number 55229 by maxmathsup by imad last updated on 19/Feb/19 $$calculate{lim}_{n\to +\mathrm{\infty }}{\int }_0^n\frac{e^{nx}}{1+{nx}^2}dx.$$ Commented by maxmathsup by imad last…

Question Number 120758 by bramlexs22 last updated on 02/Nov/20 $$\int \frac{\mathrm{dx}}{a\sin \mathrm{x}+b\cos \mathrm{x}}$$ Answered by Dwaipayan Shikari last updated on 02/Nov/20 $$\mathrm{2}\int\frac{{dt}}{{a}\left(\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }\right)+{b}\left(\frac{\mathrm{1}−{t}^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{2}} }\right)}.\frac{\mathrm{1}}{\mathrm{1}+{t}^{\mathrm{2}} }\:\:\:\:\:\:\:\:\:\:\:\:\:{tan}\frac{{x}}{\mathrm{2}}={t}…

Question Number 55214 by maxmathsup by imad last updated on 19/Feb/19 $$let{U}_n={\int }_{\frac{1}{n}}^1\sqrt{x^2+\frac{3}{n}}dx.calculate{lim}_{n\to +\mathrm{\infty }}{U}_n$$ Commented by maxmathsup by imad last…