Question Number 88357 by jagoll last updated on 10/Apr/20 $$\int\underset{\mathrm{1}} {\overset{\mathrm{4}} {\:}}\:\frac{\mathrm{dx}}{\left(\mathrm{4x}−\mathrm{1}\right)\sqrt{\mathrm{x}}} \\ $$ Commented by john santu last updated on 10/Apr/20 $$\left[\:{t}=\sqrt{{x}}\:,\:\mathrm{2}{t}\:{dt}\:=\:{dx}\:\right]\: \\ $$$$\underset{\mathrm{1}}…
Question Number 153875 by mnjuly1970 last updated on 11/Sep/21 $$ \\ $$$$\:\:\:\:\mathrm{Prove}\:\:\mathrm{that}.. \\ $$$$\:\:\: \\ $$$$\:\:\:\:\boldsymbol{\phi}\::\:=\int_{\:\mathrm{1}} ^{\:+\infty} \frac{\:{ln}\:\left({x}\:\right)}{\left(\:{x}^{\:\pi} \:−\mathrm{1}\:\right)\left(\:{ln}^{\:\mathrm{2}} \left({x}\right)\:+\mathrm{1}\:\right)^{\mathrm{2}} }{dx}=\:\frac{\pi^{\:\mathrm{2}} −\:\mathrm{8}}{\mathrm{16}}\:\:\:\:\:\:\:\:\:\blacksquare\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\: \\…
Question Number 153873 by mnjuly1970 last updated on 11/Sep/21 $$ \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \frac{\:{x}}{\left(\mathrm{1}\:+{x}^{\:\mathrm{2}} \right)\:\left(\:{e}^{\:\mathrm{2}\pi{x}} −\:\mathrm{1}\right)}\:{dx}\:=\frac{\mathrm{2}\gamma−\:\mathrm{1}}{\mathrm{4}} \\ $$$$ \\ $$ Commented by qaz last updated…
Question Number 88307 by M±th+et£s last updated on 09/Apr/20 $$\int\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{2}} −\frac{\mathrm{5}}{\mathrm{2}}{x}−\frac{\mathrm{3}}{\mathrm{2}}}\:{dx} \\ $$ Answered by TANMAY PANACEA. last updated on 09/Apr/20 $$\int\frac{\mathrm{2}{x}^{\mathrm{2}} }{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{5}{x}−\mathrm{3}}…
Question Number 88286 by Chi Mes Try last updated on 09/Apr/20 Commented by abdomathmax last updated on 09/Apr/20 $${U}_{{n}} =\left\{\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)^{{n}+\mathrm{1}} −\mathrm{1}−\frac{\mathrm{1}}{{n}}\right\}^{−{n}} \\ $$$$\Rightarrow{U}_{{n}} ={e}^{−{nln}\left\{\:\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)^{{n}+\mathrm{1}} −\mathrm{1}−\frac{\mathrm{1}}{{n}}\right\}\:\:}…
Question Number 88253 by john santu last updated on 09/Apr/20 $$\int\:\frac{\mathrm{ln}\left({x}^{\mathrm{2}} +\mathrm{1}\right)\:{dx}}{{x}+\mathrm{1}}\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 22689 by A1B1C1D1 last updated on 21/Oct/17 Answered by ajfour last updated on 25/Oct/17 $$=\int_{\mathrm{0}} ^{\:\:\mathrm{1}} \left[\int_{\mathrm{0}} ^{\:\:\mathrm{2}{x}} {e}^{{x}^{\mathrm{2}} } {dy}\right]{dx} \\ $$$$=\int_{\mathrm{0}}…
Question Number 153759 by mnjuly1970 last updated on 10/Sep/21 $$ \\ $$$$\Omega=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left\{{n}^{\mathrm{2}} \left(\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{\:{sin}^{\:\mathrm{2}} \left({x}\:\right)}{\left({sin}\left({x}\right)+{cos}\left({x}\right)\right)^{\:\mathrm{4}} }\right)^{\:{n}} {dx}\right\}=? \\ $$$$ \\ $$ Terms…
Question Number 22678 by tawa tawa last updated on 21/Oct/17 $$\int\:\frac{\mathrm{9x}^{\mathrm{4}} \:+\:\mathrm{12x}\left(\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{1}\right)}{\mathrm{2}\left(\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{1}\right)^{\mathrm{1}/\mathrm{2}} }\:\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 88206 by jagoll last updated on 09/Apr/20 $$\int\:\:\frac{\mathrm{x}+\mathrm{x}^{\mathrm{3}} }{\mathrm{1}+\mathrm{x}^{\mathrm{4}} }\:\mathrm{dx}\: \\ $$ Answered by john santu last updated on 09/Apr/20 $$=\:\int\:\frac{{x}}{\mathrm{1}+{x}^{\mathrm{4}} }\:{dx}\:+\:\int\:\frac{{x}^{\mathrm{3}} }{\mathrm{1}+{x}^{\mathrm{4}}…