Question Number 32733 by caravan msup abdo. last updated on 31/Mar/18 $${prove}\:{that}\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{1}}{\left({n}!\right)^{\mathrm{2}} }\:=\frac{\mathrm{1}}{\mathrm{2}\pi}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:{e}^{\mathrm{2}{cosx}} {dx}\:. \\ $$ Terms of Service Privacy Policy…
Question Number 32731 by caravan msup abdo. last updated on 31/Mar/18 $$\left.\mathrm{1}\right)\:{prove}\:{that}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{arctant}}{{t}}{dt}=−\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{lnt}}{\mathrm{1}+{t}^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{arctant}}{{t}}{dt}\:{at}\:{form}\:{of}\:{serie} \\ $$ Terms of…
Question Number 32724 by caravan msup abdo. last updated on 31/Mar/18 $${let}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{{n}} \sqrt{\mathrm{1}+\left(\mathrm{1}−\frac{{x}}{{n}}\right)^{{n}} }\:{dt}. \\ $$$${find}\:{a}\:{rquivalent}\:{of}\:{A}_{{n}} . \\ $$ Terms of Service Privacy…
Question Number 32729 by caravan msup abdo. last updated on 31/Mar/18 $${find}\:{lim}_{{n}\rightarrow\infty} \:\int_{\mathrm{0}} ^{{n}} \left({cos}\left(\frac{{x}}{{n}}\right)\right)^{{n}^{\mathrm{2}} } \:{dx}. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 98256 by M±th+et+s last updated on 12/Jun/20 $$\int_{\mathrm{0}} ^{\infty} \frac{{log}\left({x}\right)}{\:\sqrt{{x}}\left({x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$ Answered by mathmax by abdo last updated on 12/Jun/20 $$\mathrm{A}\:=\int_{\mathrm{0}}…
Question Number 32722 by caravan msup abdo. last updated on 31/Mar/18 $${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{3}} }\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 32720 by caravan msup abdo. last updated on 31/Mar/18 $${find}\:\int_{−\infty} ^{+\infty} \:\:\:\:\:\frac{{dt}}{\mathrm{1}\:+\left({t}+\mathrm{2}{i}\right)^{\mathrm{2}} }\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 32721 by caravan msup abdo. last updated on 31/Mar/18 $${let}\:{x}>\mathrm{0}\:{and}\:{f}\left({x}\right)=\int_{{x}} ^{+\infty} \:\:\frac{{e}^{−{t}} }{{t}}{dt} \\ $$$$\left.\mathrm{1}\right){calculate}\:{f}^{'} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{x}\rightarrow+\infty} {xf}\left({x}\right)\:{and}\:{lim}_{{x}\rightarrow\mathrm{0}^{+} } {xf}\left({x}\right). \\ $$…
Question Number 32719 by caravan msup abdo. last updated on 31/Mar/18 $${cslculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\left({t}\:−\left[{t}\right]\right){e}^{−\mathrm{3}{t}} {dt}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 163789 by amin96 last updated on 10/Jan/22 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{{arccotgh}}\left(\boldsymbol{{x}}\right)}{\mathrm{1}−\boldsymbol{{x}}^{\mathrm{2}} }\boldsymbol{{dx}}=? \\ $$$$\boldsymbol{{by}}\:\boldsymbol{{M}}.\boldsymbol{{A}} \\ $$ Commented by MJS_new last updated on 10/Jan/22 $$\mathrm{tanh}\:{x}\:=\frac{\mathrm{e}^{\mathrm{2}{x}}…