Category: Integration

Question Number 112119 by mnjuly1970 last updated on 06/Sep/20 $$\dots .calculus\dots .$$$$provethat:::$$$$if\mathrm{\Omega }={\int }_0^{1}ln\left(ln(1-\sqrt{x})\right)dx$$$$then$$$$\mathcal{R}e\left(\mathrm{\Omega }\right):=-\gamma +ln\left(2\right)\dots .$$$$$$$${m}.{n}.\:{july}\:\mathrm{1970}# \…

Question Number 177604 by mnjuly1970 last updated on 07/Oct/22 $$$$$$\mathrm{Calculate}$$$$\mathit{\varphi }={\int }_0^1\frac{\ln \left(x\right)}{1+x^2}\mathrm{d}x\stackrel{?}{=}-\mathrm{G}$$$$\sim \mathrm{Solution}\sim$$$$\:\:\:\:\:\:\boldsymbol{\phi}\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \left\{\underset{{k}=\mathrm{0}} {\overset{\infty}…

Question Number 46499 by Tawa1 last updated on 27/Oct/18 Answered by MJS last updated on 27/Oct/18 $$\int \frac{6\sin x{\cos }^{2}x+\sin 2x-23\sin x}{{(1-\cos x)}^2(5-{\sin }^{2}x)}dx=$$$$=\int\frac{\mathrm{6cos}^{\mathrm{2}} \:{x}\:+\mathrm{2cos}\:{x}\:−\mathrm{23}}{\left(\mathrm{1}−\mathrm{cos}\:{x}\right)^{\mathrm{2}} \left(\mathrm{4}+\mathrm{cos}^{\mathrm{2}} \:{x}\right)}\mathrm{sin}\:{x}\:{dx}=…

Question Number 46465 by rahul 19 last updated on 26/Oct/18 $$IfI=\frac{1}{2}{\int }_0^{\mathrm{\infty }}{t}^n{e}^{-t}dt=360.$$$$Findn?$$ Answered by tanmay.chaudhury50@gmail.com last updated on…

Question Number 46423 by maxmathsup by imad last updated on 25/Oct/18 $$calculate{\int }_0^{\mathrm{\infty }}\frac{arctan\left(x^2\right)}{1+x^2}dx$$ Terms of Service Privacy Policy Contact: info@tinkutara.com