Question Number 125962 by bramlexs22 last updated on 15/Dec/20 $$\:\:\underset{\mathrm{1}} {\overset{\mathrm{3}} {\int}}\:{x}^{\mathrm{2}{x}} \:\left(\mathrm{1}+\mathrm{ln}\:{x}\right)\:{dx}\:=?\: \\ $$ Answered by liberty last updated on 16/Dec/20 $$\:{let}\:{x}^{{x}} \:=\:{r}\:\rightarrow\begin{cases}{{x}=\mathrm{1}\rightarrow{r}=\mathrm{1}}\\{{x}=\mathrm{3}\rightarrow{r}=\mathrm{27}}\end{cases}\:\wedge\:{dr}\:=\:{x}^{{x}} \left(\mathrm{1}+\mathrm{ln}\:{x}\right){dx}…
Question Number 60424 by Mr X pcx last updated on 20/May/19 $${let}\:{z}\:\in{C}\:{and}\:\:\mid{z}\mid<\mathrm{1}\:\:{find} \\ $$$${f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{zx}\right){dx}. \\ $$ Commented by maxmathsup by imad last updated…
Question Number 60413 by tanmay last updated on 20/May/19 Commented by Meritguide1234 last updated on 21/May/19 $$\mathrm{why}\:\mathrm{do}\:\mathrm{you}\:\mathrm{post}\:\mathrm{same}\:\mathrm{question}\:\mathrm{and}\:\mathrm{solition}\:\mathrm{from}\:\mathrm{goiit}\:\mathrm{page}\:\mathrm{by}\:\mathrm{Sourav}\:\mathrm{De} \\ $$ Commented by MJS last updated on…
Question Number 125949 by Ñï= last updated on 15/Dec/20 Answered by Lordose last updated on 15/Dec/20 $$\mathrm{x}\frac{\mathrm{cos}\left(\mathrm{sint}\right)+\mathrm{cos}^{\mathrm{2}} \mathrm{t}}{\mathrm{1}+\:\mathrm{sin}\left(\mathrm{t}\right)\mathrm{sin}\left(\mathrm{sint}\right)}\:+\:\mathrm{C} \\ $$ Terms of Service Privacy Policy…
Question Number 125922 by mnjuly1970 last updated on 15/Dec/20 $$\:\:\:\:\:\:\:\:\:…{advanced}\:\:\:{calculus}… \\ $$$$\:\:\:\:\:\:\:{evaluate}\::::\:\:\:\Omega\overset{???} {=}\int_{\mathrm{0}} ^{\:\infty} {cos}\left({x}^{\mathrm{2}} \right){ln}\left({x}\right){dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\::::::::::\:\:\:\:\:\: \\ $$ Answered by mathmax by abdo…
Question Number 60384 by aliesam last updated on 20/May/19 $$\int{e}^{{coth}^{−\mathrm{1}} \left({x}\right)} \:{dx}\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 125919 by Eric002 last updated on 15/Dec/20 $$\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\infty} \frac{{dx}\:{dy}\:{dz}\:{dt}}{\left({cosh}\left({x}\right)+{cosh}\left({y}\right)+{cosh}\left({z}\right)+{cosh}\left({t}\right)\right)^{\mathrm{4}} } \\ $$$$=\frac{\mathrm{7}\zeta\left(\mathrm{3}\right)−\mathrm{6}}{\mathrm{12}} \\ $$ Terms of…
Question Number 60376 by rahul 19 last updated on 20/May/19 Commented by rahul 19 last updated on 20/May/19 $${dx}\:^{\ast} \\ $$ Commented by Mr X…
Question Number 125911 by Lordose last updated on 15/Dec/20 $$\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{xln}\left(\mathrm{1}+\mathrm{x}\right)}{\mathrm{1}+\mathrm{x}^{\mathrm{4}} }\mathrm{dx} \\ $$ Answered by mathmax by abdo last updated on 15/Dec/20 $$\mathrm{A}\:=\int_{\mathrm{0}}…
Question Number 125897 by john_santu last updated on 15/Dec/20 $$\:\:\:\int\:\frac{{dx}}{\mathrm{2}+{x}+\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\:?\: \\ $$ Commented by MJS_new last updated on 15/Dec/20 $$\mathrm{the}\:\mathrm{path}\:\mathrm{is} \\ $$$${t}=\frac{\mathrm{1}+\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{{x}}\:\Leftrightarrow\:{x}=\frac{\mathrm{2}{t}}{{t}^{\mathrm{2}} +\mathrm{1}}\:\rightarrow\:{dx}=−\frac{{x}^{\mathrm{2}}…