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Question Number 155237 Answers: 1 Comments: 0

If Ω = ∫_0 ^( ∞) (( ln^( 2) (x ).sin((√(x )) ))/x) dx prove that : Ω = 4 γ^( 2) + (π^( 3) /3) ■ m.n

$$ \\ $$$$\:\:\mathrm{I}{f}\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:{ln}^{\:\mathrm{2}} \left({x}\:\right).{sin}\left(\sqrt{{x}\:}\:\right)}{{x}}\:{dx} \\ $$$$\:\:\:\:\:{prove}\:{that}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Omega\:=\:\mathrm{4}\:\gamma^{\:\mathrm{2}} \:+\:\frac{\pi^{\:\mathrm{3}} }{\mathrm{3}}\:\:\:\:\:\blacksquare\:{m}.{n} \\ $$

Question Number 155231 Answers: 0 Comments: 0

f (x) :=(√((1/a) +x)) −(√((1/a) −x)) and D_f ≠ ∅ , g(x)=(√((ax−1)/(f^( −1) ( ax −a )))) find : D_( g) =?

$$ \\ $$$$\:\:\:{f}\:\left({x}\right)\::=\sqrt{\frac{\mathrm{1}}{{a}}\:+{x}}\:−\sqrt{\frac{\mathrm{1}}{{a}}\:−{x}} \\ $$$$\:\:{and}\:\:\:\:\mathrm{D}_{{f}} \:\neq\:\varnothing\:, \\ $$$$\:\:\:\:\:\:\:{g}\left({x}\right)=\sqrt{\frac{{ax}−\mathrm{1}}{{f}^{\:−\mathrm{1}} \left(\:{ax}\:−{a}\:\right)}} \\ $$$$\:\:\:\:\:\:\:\:{find}\::\:\:\mathrm{D}_{\:{g}} \:=? \\ $$

Question Number 155225 Answers: 0 Comments: 3

Question Number 155217 Answers: 0 Comments: 0

∫_(−∞) ^( ∞) ((ln((√(x^4 +1))))/( (√(x^4 +1)))) dx

$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{−\infty} ^{\:\infty} \:\frac{\mathrm{ln}\left(\sqrt{{x}^{\mathrm{4}} +\mathrm{1}}\right)}{\:\sqrt{{x}^{\mathrm{4}} +\mathrm{1}}}\:\:{dx} \\ $$$$\: \\ $$

Question Number 155215 Answers: 2 Comments: 0

Question Number 155212 Answers: 0 Comments: 1

Question Number 155204 Answers: 3 Comments: 0

Solve for positive integers: abcd + abc = (a+1)(b+1)(c+1)

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{positive}\:\mathrm{integers}: \\ $$$$\mathrm{abcd}\:+\:\mathrm{abc}\:=\:\left(\mathrm{a}+\mathrm{1}\right)\left(\mathrm{b}+\mathrm{1}\right)\left(\mathrm{c}+\mathrm{1}\right) \\ $$

Question Number 155203 Answers: 1 Comments: 0

Question Number 155196 Answers: 1 Comments: 2

Hi I forgot my password, is there a way I can get it ?

$${Hi}\:{I}\:{forgot}\:{my}\:{password},\: \\ $$$${is}\:{there}\:{a}\:{way}\:{I}\:{can}\:{get}\:{it}\:? \\ $$

Question Number 155194 Answers: 0 Comments: 0

Question Number 155193 Answers: 0 Comments: 0

x,y∈R^+ prove that (1/(x+y+1))−(1/((x+1)(y+1)))<(1/(11))

$$\mathrm{x},\mathrm{y}\in\mathrm{R}^{+} \:\:\mathrm{prove}\:\mathrm{that}\:\:\frac{\mathrm{1}}{\mathrm{x}+\mathrm{y}+\mathrm{1}}−\frac{\mathrm{1}}{\left(\mathrm{x}+\mathrm{1}\right)\left(\mathrm{y}+\mathrm{1}\right)}<\frac{\mathrm{1}}{\mathrm{11}} \\ $$

Question Number 155191 Answers: 0 Comments: 0

Question Number 155190 Answers: 1 Comments: 0

an atom of x with atomic number 9 has a mass of 18 with an abundsnce of 19%, a mass of 19 with an abundance of 3.5% and the remainder has a mass of 20. determine the relative mass of atom x?

$$\mathrm{an}\:\mathrm{atom}\:\mathrm{of}\:\mathrm{x}\:\mathrm{with}\:\mathrm{atomic}\:\mathrm{number}\:\mathrm{9}\:\mathrm{has}\:\:\mathrm{a}\:\mathrm{mass}\:\mathrm{of} \\ $$$$\mathrm{18}\:\mathrm{with}\:\mathrm{an}\:\mathrm{abundsnce}\:\mathrm{of}\:\mathrm{19\%},\:\mathrm{a}\:\mathrm{mass}\:\mathrm{of}\:\mathrm{19}\:\mathrm{with} \\ $$$$\mathrm{an}\:\mathrm{abundance}\:\mathrm{of}\:\mathrm{3}.\mathrm{5\%}\:\mathrm{and}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{has}\:\mathrm{a}\: \\ $$$$\mathrm{mass}\:\mathrm{of}\:\mathrm{20}.\:\mathrm{determine}\:\mathrm{the}\:\mathrm{relative}\:\mathrm{mass}\:\mathrm{of}\:\mathrm{atom}\:\mathrm{x}? \\ $$

Question Number 155189 Answers: 1 Comments: 0

How to extract the coefficient of term “x^n y^m ” in (1+((yx)/(1−x)))(1−((yx)/(1−x)))^(−1) ?

$$\mathrm{How}\:\mathrm{to}\:\mathrm{extract}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:\:\mathrm{term}\:``\mathrm{x}^{\mathrm{n}} \mathrm{y}^{\mathrm{m}} \:''\:\:\mathrm{in}\:\left(\mathrm{1}+\frac{\mathrm{yx}}{\mathrm{1}−\mathrm{x}}\right)\left(\mathrm{1}−\frac{\mathrm{yx}}{\mathrm{1}−\mathrm{x}}\right)^{−\mathrm{1}} ? \\ $$

Question Number 155183 Answers: 1 Comments: 0

Question Number 155182 Answers: 0 Comments: 0

Question Number 155180 Answers: 0 Comments: 0

Question Number 155174 Answers: 2 Comments: 0

Find n if: 133^5 +110^5 +84^5 +27^5 =n^5

$${Find}\:{n}\:{if}: \\ $$$$\mathrm{133}^{\mathrm{5}} +\mathrm{110}^{\mathrm{5}} +\mathrm{84}^{\mathrm{5}} +\mathrm{27}^{\mathrm{5}} ={n}^{\mathrm{5}} \\ $$

Question Number 155165 Answers: 1 Comments: 0

Question Number 155164 Answers: 1 Comments: 0

solve.. ⌊ (( x)/(2+ (√x))) ⌋ = 3 ( x∈ Z )

$$\:\:\:{solve}.. \\ $$$$\:\:\:\:\:\:\:\:\:\lfloor\:\frac{\:{x}}{\mathrm{2}+\:\sqrt{{x}}}\:\rfloor\:=\:\mathrm{3}\:\:\:\:\:\:\:\:\left(\:{x}\in\:\mathbb{Z}\:\right) \\ $$$$ \\ $$

Question Number 155161 Answers: 0 Comments: 0

Question Number 155159 Answers: 0 Comments: 0

∫_0 ^1 ((ln^n (x)Li_(n+1) (−x))/(1+x^2 ))dx=?

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{{ln}}^{\boldsymbol{{n}}} \left({x}\right)\boldsymbol{{Li}}_{\boldsymbol{{n}}+\mathrm{1}} \left(−{x}\right)}{\mathrm{1}+\boldsymbol{{x}}^{\mathrm{2}} }\boldsymbol{{dx}}=? \\ $$

Question Number 155154 Answers: 1 Comments: 0

let n∈N^+ solve for real numbers: x^(3n) - y^(2n) = y^(3n) - x^(2n) = 4

$$\mathrm{let}\:\:\mathrm{n}\in\mathbb{N}^{+} \:\:\mathrm{solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\mathrm{x}^{\mathrm{3}\boldsymbol{\mathrm{n}}} \:-\:\mathrm{y}^{\mathrm{2}\boldsymbol{\mathrm{n}}} \:=\:\mathrm{y}^{\mathrm{3}\boldsymbol{\mathrm{n}}} \:-\:\mathrm{x}^{\mathrm{2}\boldsymbol{\mathrm{n}}} \:=\:\mathrm{4} \\ $$

Question Number 155146 Answers: 1 Comments: 0

L=∫_0 ^1 ∫_0 ^1 ∫_0 ^1 ({(x/y)}{(y/z)}{(z/x)})^n dxdydz=?

$$\mathscr{L}=\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} \left(\left\{\frac{{x}}{{y}}\right\}\left\{\frac{{y}}{{z}}\right\}\left\{\frac{{z}}{{x}}\right\}\right)^{{n}} {dxdydz}=? \\ $$

Question Number 155144 Answers: 0 Comments: 3

how many integer solutions are there : ⌊ (1/(2+(√x)))⌋ = 3 ■

$$ \\ $$$$\:\:{how}\:{many}\:{integer}\:{solutions}\: \\ $$$$\:\:\:\:{are}\:{there}\:: \\ $$$$\:\:\:\:\lfloor\:\frac{\mathrm{1}}{\mathrm{2}+\sqrt{{x}}}\rfloor\:=\:\mathrm{3}\:\:\:\:\:\:\:\:\:\blacksquare \\ $$$$ \\ $$

Question Number 155264 Answers: 1 Comments: 0

en utilisant l′integrale de cauchy schwarz l′integrale ∫_o ^1 ((f(x))/(x+1))dx est majoree par?

$${en}\:{utilisant}\:{l}'{integrale}\:{de}\:{cauchy}\:{schwarz} \\ $$$${l}'{integrale}\:\int_{{o}} ^{\mathrm{1}} \frac{{f}\left({x}\right)}{{x}+\mathrm{1}}{dx}\:\:\:\:{est}\:{majoree}\:{par}? \\ $$$$ \\ $$

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