Question Number 44604 by arvinddayama01@gmail.com last updated on 02/Oct/18 $$\int\left[\frac{\boldsymbol{\mathrm{log}}\:\boldsymbol{\mathrm{x}}\:\:−\:\:\mathrm{1}}{\mathrm{1}+\left(\boldsymbol{\mathrm{log}}\:\boldsymbol{\mathrm{x}}\right)^{\mathrm{2}} }\right]^{\mathrm{2}} \boldsymbol{\mathrm{dx}}\:\:=\:\:\frac{\boldsymbol{\mathrm{x}}}{\left(\boldsymbol{\mathrm{log}}\:\boldsymbol{\mathrm{x}}\right)^{\mathrm{2}} +\mathrm{1}}+\boldsymbol{\mathrm{C}} \\ $$ Commented by prof Abdo imad last updated on 02/Oct/18 $${let}\:\varphi\left({x}\right)=\frac{{x}}{\mathrm{1}+\left({lnx}\right)^{\mathrm{2}}…
Question Number 44602 by arvinddayama01@gmail.com last updated on 02/Oct/18 $$\int\frac{\boldsymbol{{e}}^{\boldsymbol{\mathrm{x}}} }{\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\:\boldsymbol{\mathrm{dx}}\:=\:\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 175669 by infinityaction last updated on 04/Sep/22 $$\:\:\int\frac{\left[\mathrm{cos}^{−\mathrm{1}} {x}\left\{\sqrt{\left(\mathrm{1}−{x}^{\mathrm{2}} \right)}\right\}\right]^{−\mathrm{1}} }{\mathrm{log}_{{e}} \left\{\mathrm{1}+\left(\frac{\mathrm{sin}\left[\mathrm{2}{x}\sqrt{\left(\mathrm{1}−{x}^{\mathrm{2}} \right)}\:\right]}{\pi}\:\right\}\right.}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 44587 by maxmathsup by imad last updated on 01/Oct/18 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dt}}{\mathrm{1}+{t}^{\mathrm{2018}} } \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 02/Oct/18 Commented…
Question Number 44575 by Raj Singh last updated on 01/Oct/18 Commented by $@ty@m last updated on 01/Oct/18 $${similar}\:{to}\:{Q}.\:{No}.\:\mathrm{41703} \\ $$ Commented by Raj Singh last…
Question Number 44573 by Raj Singh last updated on 01/Oct/18 Commented by maxmathsup by imad last updated on 01/Oct/18 $${let}\:{A}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{ln}\left({sin}\left(\mathrm{2}\theta\right)\right){d}\theta\:\Rightarrow\:{A}\:=_{\mathrm{2}\theta={t}} \int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left({sin}\left({t}\right)\right)\frac{{dt}}{\mathrm{2}}…
Question Number 175614 by leodera last updated on 03/Sep/22 $$\int\frac{\mathrm{1}}{\mathrm{4}{t}^{\mathrm{3}} +\mathrm{3}{t}^{\mathrm{2}} +\mathrm{4}{t}+\mathrm{1}}{dt} \\ $$ Answered by ajfour last updated on 04/Sep/22 $${I}=\int\frac{{dt}}{\mathrm{4}\left({t}+{p}\right)\left({t}^{\mathrm{2}} +{qt}+{r}\right)} \\ $$$$\mathrm{4}{I}=\int\frac{{Adt}}{{t}+{p}}+\frac{\left({Bt}+{C}\right){dt}}{{t}^{\mathrm{2}}…
Question Number 175602 by cortano1 last updated on 03/Sep/22 $$\:\int\:\frac{\mathrm{dx}}{\mathrm{csc}\:\mathrm{x}+\:\mathrm{cos}\:\mathrm{x}}\:=? \\ $$ Commented by infinityaction last updated on 04/Sep/22 $$\:\:\int\frac{\mathrm{2}\boldsymbol{\mathrm{sin}{x}}\:}{\mathrm{2}+\mathrm{2}\boldsymbol{\mathrm{sin}{x}}.\boldsymbol{\mathrm{cos}{x}}\:}\boldsymbol{{dx}} \\ $$$${I}\:=\underset{\Psi} {\int}\frac{\left(\boldsymbol{\mathrm{sin}{x}}+\boldsymbol{\mathrm{cos}{x}}\right)\:\:\boldsymbol{{dx}}}{\:\:\mathrm{3}−\left(\boldsymbol{\mathrm{sin}{x}}−\boldsymbol{\mathrm{cos}{x}}\right)^{\mathrm{2}} \:\:}+\int_{\Phi} \frac{\left(\boldsymbol{\mathrm{sin}{x}}\:−\boldsymbol{\mathrm{cos}{x}}\right)\:\boldsymbol{{dx}}}{\mathrm{1}+\left(\boldsymbol{\mathrm{sin}{x}}+\boldsymbol{\mathrm{cos}{x}}\right)^{\mathrm{2}}…
Question Number 44515 by maxmathsup by imad last updated on 30/Sep/18 $${let}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{t}\:{ln}\left({t}\right){dt}}{\left(\mathrm{1}+{xt}\right)^{\mathrm{3}} }\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{give}\:{a}\:{explicit}\:{form}\:{of}\:{g}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{t}\:{ln}\left({t}\right)}{\left(\mathrm{1}+{t}\right)^{\mathrm{3}} }{dt} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty}…
Question Number 175583 by Linton last updated on 03/Sep/22 $$\int_{\mathrm{0}} ^{\mathrm{2}} {x}^{{t}} {dt}=\mathrm{3} \\ $$$${solve}\:{for}\:{x} \\ $$ Commented by mr W last updated on 03/Sep/22…