Question Number 222879 by MrGaster last updated on 10/Jul/25 Answered by gabthemathguy25 last updated on 10/Jul/25 $$\approx\mathrm{1}.\mathrm{67215} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 222874 by gabthemathguy25 last updated on 10/Jul/25 $$\mathrm{evaluate}\:\mathrm{the}\:\mathrm{following}\:\mathrm{integral} \\ $$$$\int\frac{{x}^{\mathrm{5}} \mathrm{ln}\left({x}\right)}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{3}} }\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 222867 by MrGaster last updated on 10/Jul/25 $$\int_{−\pi} ^{\pi} {x}\:\mathrm{sin}\:{x}\:\mathrm{cos}{nxdx} \\ $$ Answered by MrGaster last updated on 10/Jul/25 Commented by wewji12 last…
Question Number 222922 by MrGaster last updated on 10/Jul/25 $$ \\ $$$$\mathrm{Prove}:\int_{\mathrm{0}} ^{\mathrm{1}} {J}_{\mathrm{0}} \left(\mathrm{ln}\frac{\mathrm{1}}{{x}}\right){dx}=\frac{\sqrt{\mathrm{2}}}{\mathrm{2}} \\ $$ Answered by MrGaster last updated on 11/Jul/25 $${u}=\mathrm{ln}\frac{\mathrm{1}}{{x}}\Rightarrow{x}={e}^{−{u}}…
Question Number 222881 by MrGaster last updated on 10/Jul/25 $$ \\ $$$$\:\int_{\mathrm{0}} ^{\infty} {t}^{{a}} {e}^{−{t}} \mathrm{erf}\left({kt}\right){dt},{a}>\mathrm{0},{k}>\mathrm{0} \\ $$ Answered by gabthemathguy25 last updated on 10/Jul/25…
Question Number 222838 by MrGaster last updated on 09/Jul/25 $$\:\:\mathrm{Prove}:\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \frac{\mathrm{ln}\left(\mathrm{2}{x}\right)}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{dx}=−\frac{\pi^{\mathrm{2}} }{\mathrm{20}} \\ $$ Answered by MrGaster last updated on 09/Jul/25 $$ \\…
Question Number 222835 by MrGaster last updated on 09/Jul/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 222858 by MrGaster last updated on 09/Jul/25 $$\mathrm{Prove}: \\ $$$$\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \frac{\mathrm{arcsin}^{\mathrm{2}} {x}}{{x}}{dx}=\frac{\pi{i}}{\mathrm{6}}\left(\frac{\pi^{\mathrm{2}} }{\mathrm{36}}−\mathrm{Li}_{\mathrm{2}} \left(\frac{\mathrm{1}+{i}\sqrt{\mathrm{3}}}{\mathrm{2}}\right)\right)−\frac{\mathrm{1}}{\mathrm{3}}\zeta\left(\mathrm{3}\right) \\ $$ Commented by gabthemathguy25 last updated on…
Question Number 222855 by MrGaster last updated on 09/Jul/25 $$\mathrm{Prove}:\int_{−\pi} ^{\pi} {x}\:\mathrm{ln}\:\left(\mathrm{1}+\mathrm{sin}\:{x}\:+\mathrm{cos}\:{x}\right){dx}=\mathrm{2}\pi{G} \\ $$ Answered by MrGaster last updated on 09/Jul/25 Terms of Service Privacy…
Question Number 222848 by MrGaster last updated on 09/Jul/25 $$ \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{arcatn}^{\mathrm{2}} {x}}{{x}}{dx}=\frac{\pi}{\mathrm{2}}{G}−\frac{\mathrm{7}}{\mathrm{8}}\zeta\left(\mathrm{3}\right) \\ $$ Answered by MrGaster last updated on 09/Jul/25 $$\mathrm{cos}\:{x}=\underset{{n}=\mathrm{0}}…