Question Number 144924 by qaz last updated on 30/Jun/21 $$\mathrm{S}\left(\mathrm{x}\right)=\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(\mathrm{2n}\right)!!}{\left(\mathrm{2n}+\mathrm{1}\right)!!}\mathrm{x}^{\mathrm{2n}} =?……..\left(\mid\mathrm{x}\mid<\mathrm{1}\right) \\ $$ Answered by Ar Brandon last updated on 30/Jun/21 $$\left(\mathrm{2n}+\mathrm{1}\right)!!=\frac{\left(\mathrm{2n}+\mathrm{1}\right)!}{\left(\mathrm{2n}\right)!!} \\…
Question Number 144909 by ArielVyny last updated on 30/Jun/21 $$\Gamma\left({a}+{ib}\right)\:{doesn}'{t}\:{exist}\:?\:{give}\:{her}\:{value} \\ $$ Answered by qaz last updated on 30/Jun/21 $$\Gamma\left(\mathrm{a}+\mathrm{ib}\right)=\int_{\mathrm{0}} ^{\infty} \mathrm{x}^{\mathrm{a}+\mathrm{ib}−\mathrm{1}} \mathrm{e}^{−\mathrm{x}} \mathrm{dx} \\…
Question Number 144905 by SLVR last updated on 30/Jun/21 Commented by SLVR last updated on 30/Jun/21 $${kindly}\:{help}\:{me} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 79373 by mathmax by abdo last updated on 24/Jan/20 $${find}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−\left({x}^{\mathrm{3}} \:+\frac{\mathrm{1}}{{x}^{\mathrm{3}} }\right)} {dx} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 144896 by physicstutes last updated on 30/Jun/21 $$\mathrm{Evaluate}\: \\ $$$$\:\int{e}^{{x}} \left(\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}^{\mathrm{2}} }\right)^{\mathrm{2}} {dx}\: \\ $$ Answered by Dwaipayan Shikari last updated on 30/Jun/21…
Question Number 79352 by M±th+et£s last updated on 24/Jan/20 $$\int\frac{{dx}}{\mathrm{1}−\sqrt{{cos}\left({x}\right)}} \\ $$ Commented by mr W last updated on 24/Jan/20 $${no}\:{solution}\:{with}\:{elementary}\:{functions}. \\ $$$${or}\:{do}\:{you}\:{know}\:{a}\:{solution}? \\ $$…
Question Number 144876 by qaz last updated on 30/Jun/21 $$\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{x}}−\frac{\mathrm{1}}{\mathrm{x}}\right)\mathrm{dx}=\mathrm{ln}\left(\mathrm{2tan}\:\frac{\mathrm{1}}{\mathrm{2}}\right) \\ $$ Answered by mindispower last updated on 30/Jun/21 $$ \\ $$$${sin}\left({x}\right)=\frac{\mathrm{2}{tg}\left(\frac{{x}}{\mathrm{2}}\right)}{\mathrm{1}+{tg}^{\mathrm{2}} \left(\frac{{x}}{\mathrm{2}}\right)}…
Question Number 79325 by Henri Boucatchou last updated on 24/Jan/20 $$\:\boldsymbol{{Convergence}}\:\:\boldsymbol{{of}}\:: \\ $$$$\left.\:\:\mathrm{1}\right)\:\:\:\boldsymbol{{I}}=\int_{\mathrm{1}} ^{\:\infty} \frac{\boldsymbol{{e}}^{−\boldsymbol{{t}}/\mathrm{5}} \mid\boldsymbol{{sin}}\left(\boldsymbol{{lnt}}\right)\mid}{\left(\boldsymbol{{t}}−\mathrm{1}\right)^{\mathrm{3}/\mathrm{2}} }\boldsymbol{{dt}} \\ $$$$\left.\:\:\mathrm{2}\right)\:\:\:\boldsymbol{{I}}=\int_{\mathrm{1}} ^{\infty} \frac{\sqrt{\boldsymbol{{lnx}}}}{\left(\boldsymbol{{x}}−\mathrm{1}\right)\sqrt{\boldsymbol{{x}}}}\boldsymbol{{dx}} \\ $$ Commented by…
Question Number 144813 by mnjuly1970 last updated on 29/Jun/21 $$ \\ $$$$\:\:\:\:\:\:\mathrm{I}:=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{ln}\:\left({x}\right)}{\mathrm{1}\:+\:{x}^{\:\mathrm{2}} }\:{dx} \\ $$$$\:\:\:\:\:\:\:\:\::=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \mathrm{ln}\left({x}\:\right)\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{\:{n}} \:{x}^{\:\mathrm{2}{n}} \:{dx} \\ $$$$\:\:\:\:\:\:\:\::=\:\underset{{n}=\mathrm{0}}…
Question Number 144815 by mnjuly1970 last updated on 29/Jun/21 Answered by mindispower last updated on 30/Jun/21 $$=\int_{\mathrm{0}} ^{\infty} \frac{{sin}\left({x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right)+{sin}\left(\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }−{x}\right)}{\mathrm{2}\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:}{dx} \\ $$$${x}={sh}\left({t}\right) \\…