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Category: Integration

1-3-x-2x-1-ln-x-dx-

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-60413

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-125949

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…

0-0-0-0-dx-dy-dz-dt-cosh-x-cosh-y-cosh-z-cosh-t-4-7-3-6-12-

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…

dx-2-x-1-x-2-

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}}…