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Question Number 137518 Answers: 1 Comments: 0

Ω = ∫_0 ^( ∞) ((u^2 +2)/(u^4 +2u^2 +2))du

$$\Omega\:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{u}^{\mathrm{2}} +\mathrm{2}}{\mathrm{u}^{\mathrm{4}} +\mathrm{2u}^{\mathrm{2}} +\mathrm{2}}\mathrm{du} \\ $$

Question Number 137509 Answers: 2 Comments: 1

∫ ((sin ((√x) )+cos ((√x) ))/( (√x) sin (2(√x) ))) dx

$$\int\:\frac{\mathrm{sin}\:\left(\sqrt{{x}}\:\right)+\mathrm{cos}\:\left(\sqrt{{x}}\:\right)}{\:\sqrt{{x}}\:\mathrm{sin}\:\left(\mathrm{2}\sqrt{{x}}\:\right)}\:{dx}\: \\ $$

Question Number 137508 Answers: 2 Comments: 0

∫ ((sin ((1/x)))/x^3 ) dx =?

$$\int\:\frac{\mathrm{sin}\:\left(\frac{\mathrm{1}}{{x}}\right)}{{x}^{\mathrm{3}} }\:{dx}\:=? \\ $$

Question Number 137501 Answers: 1 Comments: 0

....advanced .... calculus.... prove that:: 𝛗=∫_0 ^( 1) ((ln(x).ln(1−x))/(1+x))dx=((13)/8)ζ(3)−(π^2 /4)ln(2)....

$$\:\:\:\:\:\:\:....{advanced}\:....\:{calculus}.... \\ $$$$\:\:{prove}\:{that}:: \\ $$$$\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left({x}\right).{ln}\left(\mathrm{1}−{x}\right)}{\mathrm{1}+{x}}{dx}=\frac{\mathrm{13}}{\mathrm{8}}\zeta\left(\mathrm{3}\right)−\frac{\pi^{\mathrm{2}} }{\mathrm{4}}{ln}\left(\mathrm{2}\right).... \\ $$

Question Number 137482 Answers: 2 Comments: 0

Question Number 137477 Answers: 1 Comments: 1

Question Number 137476 Answers: 1 Comments: 2

Question Number 137474 Answers: 3 Comments: 0

.....nice ........ calculus..... 𝛗=∫_0 ^( 1) ln(((ln((√(1−x)))))^(1/3) ) Im(𝛗)=???

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:.....{nice}\:\:........\:\:{calculus}..... \\ $$$$\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} {ln}\left(\sqrt[{\mathrm{3}}]{{ln}\left(\sqrt{\mathrm{1}−{x}}\right)}\:\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{Im}\left(\boldsymbol{\phi}\right)=??? \\ $$

Question Number 137473 Answers: 2 Comments: 0

what is larger? 99^(100) or 100^(99) ?

$${what}\:{is}\:{larger}?\:\mathrm{99}^{\mathrm{100}} \:{or}\:\mathrm{100}^{\mathrm{99}} ? \\ $$

Question Number 137472 Answers: 1 Comments: 0

solve x^3 −2[x]=5

$${solve} \\ $$$${x}^{\mathrm{3}} −\mathrm{2}\left[{x}\right]=\mathrm{5} \\ $$

Question Number 137470 Answers: 0 Comments: 0

Question Number 137469 Answers: 0 Comments: 0

Question Number 137468 Answers: 1 Comments: 0

Find the value of (cos 1°+isin 1°)(cos 2°+isin 2°)…(cos 359°+isin 359°).

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\left(\mathrm{cos}\:\mathrm{1}°+{i}\mathrm{sin}\:\mathrm{1}°\right)\left(\mathrm{cos}\:\mathrm{2}°+{i}\mathrm{sin}\:\mathrm{2}°\right)\ldots\left(\mathrm{cos}\:\mathrm{359}°+{i}\mathrm{sin}\:\mathrm{359}°\right). \\ $$

Question Number 137467 Answers: 1 Comments: 0

Question Number 137466 Answers: 0 Comments: 0

Ω = ∫_0 ^( 1) ((xtan^(−1) (x)log(x))/(1+x^2 ))dx

$$\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{xtan}^{−\mathrm{1}} \left(\mathrm{x}\right)\mathrm{log}\left(\mathrm{x}\right)}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx} \\ $$

Question Number 137461 Answers: 3 Comments: 0

Question Number 137458 Answers: 0 Comments: 0

Question Number 137448 Answers: 2 Comments: 0

∫_0 ^( 3/4) (dx/((x+1)(√(x^2 +1)))) ?

$$\int_{\mathrm{0}} ^{\:\mathrm{3}/\mathrm{4}} \frac{{dx}}{\left({x}+\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}\:? \\ $$

Question Number 137439 Answers: 2 Comments: 0

......nice calculus..... prove that:: 𝛘=∫_0 ^( 1) ((ln(x+(√(1−x^2 )) ))/x)dx=(π^2 /(16)) ....

$$\:\:\:\:\:\:\:\:\:\:\:\:......{nice}\:\:{calculus}..... \\ $$$$\:\:\:\:{prove}\:{that}:: \\ $$$$\:\:\:\:\:\:\boldsymbol{\chi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left({x}+\sqrt{\mathrm{1}−{x}^{\mathrm{2}} \:}\:\right)}{{x}}{dx}=\frac{\pi^{\mathrm{2}} }{\mathrm{16}}\:.... \\ $$

Question Number 137437 Answers: 2 Comments: 0

Question Number 137435 Answers: 0 Comments: 4

Question Number 137429 Answers: 0 Comments: 4

A nuclide _(81)^(210) X decays to another nuclide _(80)^A Y in four successive radioactive decays. Each decay involves the emmision of either an alpha particle or a beta particle. The value of A is: A. 120 B. 206 C. 208 D. 212

$$\mathrm{A}\:\mathrm{nuclide}\:_{\mathrm{81}} ^{\mathrm{210}} {X}\:\mathrm{decays}\:\mathrm{to}\:\mathrm{another}\:\mathrm{nuclide}\:_{\mathrm{80}} ^{{A}} {Y}\:\mathrm{in}\: \\ $$$$\mathrm{four}\:\mathrm{successive}\:\mathrm{radioactive}\:\mathrm{decays}.\:\mathrm{Each}\:\mathrm{decay} \\ $$$$\mathrm{involves}\:\mathrm{the}\:\mathrm{emmision}\:\mathrm{of}\:\mathrm{either}\:\mathrm{an}\:\mathrm{alpha}\:\mathrm{particle} \\ $$$$\mathrm{or}\:\mathrm{a}\:\mathrm{beta}\:\mathrm{particle}.\:\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:{A}\:\mathrm{is}: \\ $$$$\mathrm{A}.\:\mathrm{120}\:\:\:\:\:\:\:\:\:\:\:\mathrm{B}.\:\mathrm{206} \\ $$$$\mathrm{C}.\:\mathrm{208}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{D}.\:\mathrm{212} \\ $$

Question Number 137420 Answers: 0 Comments: 1

......mathematical ... ... ... analysis(II)..... prove that :: Ω=∫_( R) (Σ_(n=0) ^∞ (((−x^2 )^n )/((n!)^2 )))dx=1 ..........................

$$\:\:\:\:\:\:\:\:\:\:\:\:\:......{mathematical}\:...\:...\:...\:{analysis}\left({II}\right)..... \\ $$$$\:\:\:\:\:\:\:{prove}\:\:{that}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\Omega=\int_{\:\mathbb{R}} \left(\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−{x}^{\mathrm{2}} \right)^{{n}} }{\left({n}!\right)^{\mathrm{2}} }\right){dx}=\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:.......................... \\ $$

Question Number 137419 Answers: 1 Comments: 0

.........mathematical .... analysis........ evaluate.... 𝛗=∫_0 ^( ∞) ((e^(2πx) −e^(πx) )/(x(1+e^(2πx) )(1+e^(πx) )))dx=λ∫_0 ^( 1) ln(Γ(x)dx λ = ???

$$\:\:\:\:\:\:\:.........{mathematical}\:\:\:\:....\:\:\:{analysis}........ \\ $$$$\:\:\:\:\:\:\:{evaluate}.... \\ $$$$\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{e}^{\mathrm{2}\pi{x}} −{e}^{\pi{x}} }{{x}\left(\mathrm{1}+{e}^{\mathrm{2}\pi{x}} \right)\left(\mathrm{1}+{e}^{\pi{x}} \right)}{dx}=\lambda\int_{\mathrm{0}} ^{\:\mathrm{1}} {ln}\left(\Gamma\left({x}\right){dx}\right. \\ $$$$\:\:\:\:\:\:\:\:\:\:\lambda\:=\:??? \\ $$$$\:\:\:\:\:\: \\ $$

Question Number 137415 Answers: 2 Comments: 4

solve x+(√(x(x+1)))+(√(x(x+2)))+(√((x+1)(x+2)))=2

$${solve} \\ $$$${x}+\sqrt{{x}\left({x}+\mathrm{1}\right)}+\sqrt{{x}\left({x}+\mathrm{2}\right)}+\sqrt{\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)}=\mathrm{2} \\ $$

Question Number 137412 Answers: 1 Comments: 0

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