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1-x-1-x-1-x-dx-

Question Number 62907 by aliesam last updated on 26/Jun/19 $$\int\sqrt{\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}\:}\left(\mathrm{1}+{x}\right)\:{dx} \\ $$ Commented by mathmax by abdo last updated on 26/Jun/19 $${let}\:{A}\:=\int\sqrt{\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}}\left(\mathrm{1}+{x}\right){dx}\:{changement}\:{x}\:={cos}\left(\mathrm{2}\theta\right)\:{give}\:\mathrm{2}\theta\:={arcosx}\:\Rightarrow \\ $$$${A}\:=\int\:\sqrt{\frac{\mathrm{2}{cos}^{\mathrm{2}} \left(\theta\right)}{\mathrm{2}{sin}^{\mathrm{2}}…

y-x-x-2-

Question Number 128382 by arash sharifi last updated on 06/Jan/21 $${y}={x}^{{x}^{\mathrm{2}} } \\ $$ Commented by hknkrc46 last updated on 06/Jan/21 $$\bullet\:\boldsymbol{{x}}\:\in\:\mathbb{R}\:\Rightarrow\:\boldsymbol{{y}}\:\in\:\mathbb{R} \\ $$$$\bullet\:\boldsymbol{{x}}\:=\:\mp\mathrm{1}\:\Rightarrow\:\boldsymbol{{y}}\:=\:\mathrm{1} \\…

Prove-n-0-a-n-b-n-c-n-n-c-c-a-b-c-a-c-b-Where-a-n-k-0-n-1-k-a-

Question Number 128321 by Dwaipayan Shikari last updated on 06/Jan/21 $${Prove} \\ $$$$\underset{{n}\geqslant\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left({a}\right)_{{n}} \left({b}\right)_{{n}} }{\left({c}\right)_{{n}} {n}!}=\frac{\Gamma\left({c}\right)\Gamma\left({c}−{a}−{b}\right)}{\Gamma\left({c}−{a}\right)\Gamma\left({c}−{b}\right)} \\ $$$${Where}\:\left({a}\right)_{{n}} =\underset{{k}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\prod}}\left({k}+{a}\right) \\ $$…

An-element-X-has-RAM-of-88g-when-a-current-of-0-5A-was-passed-through-fused-chloride-of-X-for-32minutes-and-10sec-0-44g-of-X-was-deposited-at-the-cathode-a-number-of-faraday-b-write-formular-of-X

Question Number 62750 by peter frank last updated on 24/Jun/19 $${An}\:{element}\:{X}\:{has}\:{RAM} \\ $$$${of}\:\mathrm{88}{g}.{when}\:{a}\:{current} \\ $$$${of}\:\mathrm{0}.\mathrm{5}{A}\:{was}\:{passed}\:{through} \\ $$$${fused}\:{chloride}\:{of}\:{X}\:{for} \\ $$$$\mathrm{32}{minutes}\:{and}\:\mathrm{10}{sec}. \\ $$$$\mathrm{0}.\mathrm{44}{g}\:{of}\:{X}\:{was}\:{deposited} \\ $$$${at}\:{the}\:{cathode} \\ $$$$\left({a}\right){number}\:{of}\:{faraday}?…

1-1-2-1-1-2-2-1-3-2-1-3-2-2-2-1-4-3-1-3-5-2-3-2-4-pi-Prove-the-above-Relation-

Question Number 128256 by Dwaipayan Shikari last updated on 05/Jan/21 $$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}!\mathrm{1}!}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{3}!\mathrm{2}!}\left(\frac{\mathrm{1}.\mathrm{3}}{\mathrm{2}^{\mathrm{2}} }\right)^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{4}!\mathrm{3}!}\left(\frac{\mathrm{1}.\mathrm{3}.\mathrm{5}}{\mathrm{2}^{\mathrm{3}} }\right)^{\mathrm{2}} +….=\frac{\mathrm{4}}{\pi} \\ $$$${Prove}\:{the}\:{above}\:{Relation} \\ $$ Commented by Dwaipayan Shikari last…