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Category: Integration

Question-59960

Question Number 59960 by cesar.marval.larez@gmail.com last updated on 16/May/19 Answered by MJS last updated on 16/May/19 $$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{understand}\:\mathrm{the}\:\mathrm{question} \\ $$$$\mathrm{is}\:{A}\:\mathrm{the}\:\mathrm{source}\:\mathrm{or}\:\mathrm{the}\:\mathrm{target}\:\mathrm{of}\:\mathrm{the}\:\mathrm{vectors}? \\ $$$$\mathrm{if}\:\mathrm{it}'\mathrm{s}\:\mathrm{the}\:\mathrm{source} \\ $$$${X}={A}+\overset{\rightarrow} {\mathfrak{v}}=\left({a},\:{b}\right)+\left({v},\:{w}\right)=\left({a}+{v},\:{b}+{w}\right) \\…

Question-59946

Question Number 59946 by Sardor2211 last updated on 16/May/19 Commented by maxmathsup by imad last updated on 17/May/19 $${let}\:{use}\:{the}\:{chang}\:\:\mathrm{1}+\left({x}+\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} \:={t}\:\Rightarrow\left({x}+\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} \:={t}−\mathrm{1}\:\Rightarrow{x}+\mathrm{1}\:=\left({t}−\mathrm{1}\right)^{\mathrm{3}} \:\Rightarrow \\ $$$$\int_{−\mathrm{1}} ^{\mathrm{0}}…

advanced-calculus-prove-that-I-1-t-4-6t-2-1-ln-ln-t-1-t-2-3-dt-2G-pi-G-catalan-constant-

Question Number 125462 by mnjuly1970 last updated on 11/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…\:\clubsuit{advanced}\:\:{calculus}\clubsuit… \\ $$$$\:\:\:\blacklozenge\blacklozenge\:{prove}\:{that}: \\ $$$$\:\:\:\:\:\mathrm{I}=\int_{\mathrm{1}} ^{\:\infty} \frac{\left({t}^{\mathrm{4}} −\mathrm{6}{t}^{\mathrm{2}} +\mathrm{1}\right){ln}\left({ln}\left({t}\right)\right)}{\left(\mathrm{1}+{t}^{\mathrm{2}} \right)^{\mathrm{3}} }{dt}=\frac{\mathrm{2G}}{\pi} \\ $$$$\:\:\mathrm{G}\::\:\:{catalan}\:\:{constant}… \\ $$ Answered…

advanced-calculus-evaluate-n-2-2n-2-n-

Question Number 125458 by mnjuly1970 last updated on 11/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{advanced}\:\:{calculus}… \\ $$$$\:\:\:\:\:\:\:\:{evaluate}\:::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\left\{\:\frac{\zeta\:\left(\mathrm{2}{n}\:\right)}{\mathrm{2}^{\:{n}} }\:\right\}\:=?? \\ $$$$ \\ $$ Answered by Dwaipayan Shikari…