Category: Integration

Question Number 55267 by maxmathsup by imad last updated on 25/Feb/19 $$1)calculatef\left(x\right)={\int }_0^{\frac{\pi }{4}}ln(1+xtan\theta )d\theta$$$$2)findthevaluesofintegrals{\int }_0^{\frac{\pi }{4}}ln(1+tan\theta )and{\int }_0^{\frac{\pi }{4}}ln(1+2tan\theta )d\theta .$$$$\left.\mathrm{1}\right)\:{we}\:{have}\:{f}^{'} \left({x}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\:\frac{{tan}\theta}{\mathrm{1}+{xtan}\theta}\:{d}\theta\:=\int_{\mathrm{0}}…

Question Number 120774 by mnjuly1970 last updated on 02/Nov/20 $$\dots advancedcalculus\dots$$$$provethat::$$$$\mathrm{\Omega }={\int }_0^1\frac{ln\left(x\right)}{\sqrt[3]{1-x^3}}dx\stackrel{???}{=}-\frac{\pi }{3\sqrt{3}}(ln\left(3\right)+\frac{\pi }{3\sqrt{3}})$$$$\dots m.n.1970\dots$$ Answered by mindispower…

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…