Question Number 60938 by aliesam last updated on 27/May/19 $$\int\frac{{csc}^{\mathrm{2019}} \left({x}\right)}{{sec}^{\mathrm{5}} \left({x}\right)}\:{tan}^{\mathrm{2}} \left({x}\right)\:{dx} \\ $$ Commented by Prithwish sen last updated on 27/May/19 $$\int\frac{\mathrm{cos}^{\mathrm{3}} \mathrm{x}}{\mathrm{sin}^{\mathrm{2017}}…
Question Number 126465 by mnjuly1970 last updated on 20/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:…\:{nice}\:\:{calculus}… \\ $$$$\:\:\:\:\:\mathscr{E}{valuate}\:… \\ $$$$\:\:\:\:\:\:\:\:\phi\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{sin}\left({ln}\left({x}\right)\right)−{ln}\left({x}\right)}{{ln}^{\mathrm{2}} \left({x}\right)}{dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathscr{A}{ns}\:::\:{ln}\left(\sqrt{\mathrm{2}}\:\right)+\frac{\pi}{\mathrm{4}}\:−\mathrm{1}\:… \\ $$ Commented by talminator2856791 last…
Question Number 60901 by maxmathsup by imad last updated on 27/May/19 $${find}\:\int\:\:{arctan}\left(\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} }\right){dx}\: \\ $$ Answered by perlman last updated on 27/May/19 $${integrat}\:{by}\left[{part}\right. \\ $$$$={xarctan}\left(\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}}…
Question Number 60894 by mathsolverby Abdo last updated on 26/May/19 $${study}\:{the}\:{convergence}\:{of}\: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\sqrt{\mathrm{1}+\mathrm{2}{x}}−\sqrt{\mathrm{1}+{x}}}{{ln}\left(\mathrm{1}+{x}\right)}{dx}\:\:{and}\:{determine}\:{its} \\ $$$${value}. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 60893 by mathsolverby Abdo last updated on 26/May/19 $${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{dx}}{\:\sqrt{\mathrm{2}}{cos}^{\mathrm{2}} {x}\:+\sqrt{\mathrm{3}}{sin}^{\mathrm{2}} {x}} \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 126427 by Study last updated on 20/Dec/20 $${li}\underset{{x}\rightarrow−\mathrm{3}} {{m}}\frac{\mid{x}+\mathrm{3}\mid}{{x}+\mathrm{3}}\:\:\:\:\:\:{show}\:{right}\:{and}\:{left}\:{side} \\ $$$${limit}?? \\ $$ Answered by liberty last updated on 20/Dec/20 $$\underset{{x}\rightarrow−\mathrm{3}^{−} } {\mathrm{lim}}\left[\:\frac{\mid{x}+\mathrm{3}\mid}{{x}+\mathrm{3}}\:\right]\:=\:\underset{{x}\rightarrow−\mathrm{3}^{−}…
Question Number 60881 by aliesam last updated on 26/May/19 $$\underset{−\pi} {\overset{\pi} {\int}}{sin}\left(\frac{\mathrm{1}}{\mathrm{1}−{x}^{\mathrm{2}} }\right)\:{dx} \\ $$ Commented by MJS last updated on 26/May/19 $$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{think}\:\mathrm{we}\:\mathrm{can}\:\mathrm{solve}\:\mathrm{this},\:\mathrm{not}\:\mathrm{even} \\ $$$$\mathrm{approximate}.\:\mathrm{it}'\mathrm{s}\:\mathrm{undefined}\:\mathrm{at}\:{x}=\pm\mathrm{1}\:\mathrm{and}…
Question Number 191921 by Rupesh123 last updated on 03/May/23 Answered by AST last updated on 03/May/23 $$\int\left(\mathrm{3}{x}+\mathrm{5}\right){dx}=\frac{\mathrm{3}{x}^{\mathrm{2}} }{\mathrm{2}}+\mathrm{5}{x}+{c} \\ $$$$\int_{−\mathrm{4}} ^{\mathrm{2}} \left(\mathrm{3}{x}+\mathrm{5}\right){dx}=\left(\mathrm{16}+{c}\right)−\left(\mathrm{4}+{c}\right)=\mathrm{12} \\ $$$$\Rightarrow\left(\mathrm{4}+{log}_{\mathrm{3}} {x}\right)\left({log}_{\mathrm{3}}…
Question Number 126383 by Lordose last updated on 20/Dec/20 $$\mathrm{Evaluate}\:\Omega\:\mathrm{if} \\ $$$$\:\:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{cos}\left(\mathrm{mx}\right)}{\mathrm{x}^{\mathrm{4}} +\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\mathrm{dx} \\ $$ Answered by mathmax by abdo last updated…
Question Number 126369 by I want to learn more last updated on 19/Dec/20 $$\int\:\frac{\mathrm{tan}\left(\mathrm{x}\right)}{\mathrm{x}}\:\:\mathrm{dx} \\ $$ Answered by Olaf last updated on 20/Dec/20 $$\mathrm{I}\:\mathrm{believe}\:\mathrm{the}\:\mathrm{only}\:\mathrm{way}\:\mathrm{to}\:\mathrm{handle}\:\mathrm{this} \\…