Question Number 147474 by mnjuly1970 last updated on 21/Jul/21 Answered by mindispower last updated on 21/Jul/21 $$\frac{\mathrm{1}}{\mathrm{2}{a}}\left(\underset{{n}\geqslant−\infty} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{4}{n}−{a}}−\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{4}{n}+{a}}\right)=\underset{{n}\geqslant−\infty} {\sum}\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{16}{n}^{\mathrm{2}} −{a}^{\mathrm{2}} }={f}\left({a}\right)…
Question Number 147411 by mnjuly1970 last updated on 20/Jul/21 Answered by mnjuly1970 last updated on 20/Jul/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\::\overset{\sqrt{{x}}\::=\:{y}} {=}\:\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{2}{y}\:{dy}}{\mathrm{1}+{e}^{\:{y}} }\:=\mathrm{2}\:\int_{\mathrm{0}} ^{\:\infty} \frac{{ydy}}{\mathrm{1}+{e}^{\:{y}} } \\…
Question Number 81835 by M±th+et£s last updated on 15/Feb/20 Commented by M±th+et£s last updated on 15/Feb/20 $${hn}:\:{harmonic}\:{number} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 147355 by legand last updated on 20/Jul/21 Answered by ArielVyny last updated on 20/Jul/21 $${the}\:{question}\:{is}\:{not}\:{complete}\:{sir} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 147346 by mnjuly1970 last updated on 20/Jul/21 Answered by qaz last updated on 20/Jul/21 $$\mathrm{a}_{\mathrm{n}} =\mathrm{2}\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \left(\mathrm{1}−\mathrm{sin}\:\mathrm{x}\right)^{\mathrm{n}} \mathrm{sin}\:\mathrm{xd}\left(\mathrm{sin}\:\mathrm{x}\right) \\ $$$$\Rightarrow\mathrm{a}_{\mathrm{n}} =\mathrm{2}\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 147262 by mnjuly1970 last updated on 19/Jul/21 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…#\:\:\mathrm{Calculus}\:#… \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}\::=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \mathrm{Li}_{\:\mathrm{2}} \:\left({x}^{\:\mathrm{2}} \right)\:{dx}\:=\:? \\ $$$$ \\ $$$$ \\…
Question Number 147209 by alcohol last updated on 18/Jul/21 Commented by Ar Brandon last updated on 19/Jul/21 $$\mathrm{1}.\int_{−\mathrm{a}} ^{\mathrm{a}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}=\int_{−\mathrm{a}} ^{\mathrm{0}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}+\int_{\mathrm{0}} ^{\mathrm{a}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx} \\…
Question Number 147135 by puissant last updated on 18/Jul/21 Answered by gsk2684 last updated on 18/Jul/21 $${let}\:{y}={x}^{{x}^{{x}^{.} } } \:{then}\:{y}={x}^{{y}} \\ $$$$\mathrm{ln}\:{y}\:=\:{y}\:\mathrm{ln}\:{x} \\ $$$$\frac{\mathrm{1}}{{y}}\:\frac{{dy}}{{dx}}={y}\:\frac{\mathrm{1}}{{x}}\:+\:\frac{{dy}}{{dx}}\:\mathrm{ln}\:{x} \\…
Question Number 81586 by jagoll last updated on 14/Feb/20 $${Dear}\:{mister}\: \\ $$$${Tanmay} \\ $$$${y}\:''\:−\:{y}'\:−\mathrm{6}{y}\:=\:\mathrm{2sin}\:\mathrm{3}{x}\: \\ $$$${find}\:{solution} \\ $$$$\: \\ $$$${let}\:{y}\:=\:{e}^{{mx}} \:?\:{or}\:{not}\: \\ $$$$ \\ $$…
Question Number 81565 by jagoll last updated on 14/Feb/20 $${If}\:{f}\left({x}\right)=\:\left(\mathrm{tan}\:{x}\right)^{\mathrm{cot}\:{x}} \:+\:\left(\mathrm{cot}\:{x}\right)^{\mathrm{tan}\:{x}} \\ $$$${f}\:'\left({x}\right)=\:? \\ $$ Commented by john santu last updated on 14/Feb/20 $$\mathrm{good}\:\mathrm{question} \\…