Question Number 138516 by mnjuly1970 last updated on 14/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:………..{calculus}\:…\:…\:…\:\left(\mathrm{I}\right)……… \\ $$$$\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{xe}^{{x}} }{\left(\mathrm{1}+{e}^{{x}} \right)^{\mathrm{3}} }{dx}\:=? \\ $$$$\:\:\:\:\:\:\:=\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\:\infty} {x}.{d}\left(\frac{−\mathrm{1}}{\left(\mathrm{1}+{e}^{{x}} \right)^{\mathrm{2}} }\:\right) \\ $$$$\:\:\:\:\:\:\:=\frac{\mathrm{1}}{\mathrm{2}}\left[\frac{−{x}}{\left(\mathrm{1}+{e}^{{x}}…
Question Number 7422 by Tawakalitu. last updated on 28/Aug/16 $$\int\frac{{x}^{\mathrm{2}} \:{dx}}{\left({x}\:−\:\mathrm{1}\right)\left({x}^{\mathrm{2}} \:+\:\mathrm{4}\right)^{\mathrm{2}} } \\ $$ Answered by Yozzia last updated on 28/Aug/16 $$\frac{{x}^{\mathrm{2}} }{\left({x}−\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{4}\right)^{\mathrm{2}}…
Question Number 138485 by SLVR last updated on 14/Apr/21 Commented by SLVR last updated on 14/Apr/21 $${Good}\:{morning}\:{mr}.{W}\:{thanks}\:{for} \\ $$$${your}\:{support}\:.{The}\:{above}\:{is}\:{also}\:{i} \\ $$$${missed}\:{long}\:{ago}..{and}\:{i}\:{couldnot} \\ $$$${retrive}\:{from}\:{the}\:{group}.{kindly}\:{help} \\ $$…
Question Number 7397 by Tawakalitu. last updated on 26/Aug/16 Answered by sandy_suhendra last updated on 27/Aug/16 $${sin}\:{x}\:=\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} \:{x}^{\mathrm{2}{n}+\mathrm{1}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)!} \\ $$$$\frac{\mathrm{1}}{{x}}\:{sin}\:{x}\:=\:\frac{\mathrm{1}}{{x}}\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}}…
Question Number 138460 by mnjuly1970 last updated on 13/Apr/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 7385 by Tawakalitu. last updated on 25/Aug/16 $$\int{sin}\left(\mathrm{101}{x}\right)\:.\:{sin}^{\mathrm{90}} \left({x}\right)\:{dx} \\ $$ Commented by Yozzia last updated on 26/Aug/16 $${Let}\:{I}\left({n}\right)=\int{e}^{\mathrm{101}{ix}} {sin}^{{n}} {xdx}\:\:\:\left({n}\in\mathbb{Z}^{\geqslant} \:{i}=\sqrt{−\mathrm{1}}\right) \\…
Question Number 138428 by tugu last updated on 13/Apr/21 $${what}\:{the}\:{area}\:{of}\:\:{area}\:{bounded}\:{by}\:{line} \\ $$$${y}=\:\mid{ln}\:{x}\mid\:{and}\:{y}=\:\mathrm{2}\: \\ $$ Answered by Ñï= last updated on 13/Apr/21 $$\mid{lnx}\mid=\mathrm{2} \\ $$$$\Rightarrow{x}={e}^{\mathrm{2}} ,{e}^{−\mathrm{2}}…
Question Number 72889 by mathmax by abdo last updated on 04/Nov/19 $${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{\left(\mathrm{2}{n}+\mathrm{1}\right){n}^{\mathrm{2}} } \\ $$ Commented by mathmax by abdo last updated…
Question Number 72888 by mathmax by abdo last updated on 04/Nov/19 $${let}\:{f}\left({x}\right)=\int_{\frac{\pi}{\mathrm{6}}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{tant}}{\mathrm{2}+{x}\:{cost}}{dt}\:\:{with}\:{x}\:{real} \\ $$$$\left.\mathrm{1}\right){determine}\:{a}\:{explicit}\:{form}\:{for}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){determine}\:{also}\:{g}\left({x}\right)=\int_{\frac{\pi}{\mathrm{6}}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{tant}}{\left(\mathrm{2}+{xcost}\right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\frac{\pi}{\mathrm{6}}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{tant}}{\left(\mathrm{2}+\mathrm{3}{cost}\right)}{dt}\:{and}\:\int_{\frac{\pi}{\mathrm{6}}}…
Question Number 138424 by tugu last updated on 13/Apr/21 $$\mid\underset{\mathrm{1}} {\overset{\sqrt{\mathrm{3}}} {\int}}\:\frac{{e}^{−{x}} {sin}\:{x}}{{x}^{\mathrm{2}} +\mathrm{1}}{dx}\mid\leqslant\frac{\pi}{\mathrm{12}{e}} \\ $$ Commented by mitica last updated on 14/Apr/21 $$\exists{c}\in\left[\mathrm{1},\sqrt{\mathrm{3}}\right],\underset{\mathrm{1}} {\overset{\sqrt{\mathrm{3}}}…