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Author: Tinku Tara

Question-192883

Question Number 192883 by ajfour last updated on 30/May/23 Answered by ajfour last updated on 30/May/23 $$\left({p}+{s}\right)^{\mathrm{3}} −\left({p}+{s}\right)={k} \\ $$$${p}^{\mathrm{3}} −{p}={c} \\ $$$${s}\left\{\left({p}+{s}\right)^{\mathrm{2}} +{p}^{\mathrm{2}} +{p}\left({p}+{s}\right)\right\}−{s}={k}−{c}…

S-n-4-n-1-1-n-2-

Question Number 127344 by bobhans last updated on 29/Dec/20 $${S}\:=\:\underset{{n}=\mathrm{4}} {\overset{\infty} {\sum}}\ell{n}\:\left(\mathrm{1}−\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\right)\:=?\: \\ $$ Answered by liberty last updated on 29/Dec/20 $$\:{S}\:=\:\underset{{n}=\mathrm{4}} {\overset{\infty} {\sum}}\mathrm{ln}\:\left(\mathrm{1}−\frac{\mathrm{1}}{{n}^{\mathrm{2}}…

Question-61809

Question Number 61809 by aliesam last updated on 09/Jun/19 Commented by maxmathsup by imad last updated on 10/Jun/19 $${let}\:{A}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{x}^{{n}} }{\:\sqrt{{ln}\left({x}\right)}}\:{dx}\:\Rightarrow\:{A}\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{x}^{{n}} }{\:\sqrt{−\left(−{lnx}\right)}}\:{dx}\:=\frac{\mathrm{1}}{\:\sqrt{−\mathrm{1}}}\:\int_{\mathrm{0}}…