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Question Number 65003 Answers: 0 Comments: 0

find ∫_0 ^∞ (dx/(Γ(x))) with Γ(x) =∫_0 ^∞ t^(x−1) e^(−t) dt (x>0)

$${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\Gamma\left({x}\right)}\:\:{with}\:\:\Gamma\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:{t}^{{x}−\mathrm{1}} \:{e}^{−{t}} \:{dt}\:\:\:\left({x}>\mathrm{0}\right) \\ $$

Question Number 64994 Answers: 1 Comments: 1

∫(√(tanh(x))) dx

$$\int\sqrt{{tanh}\left({x}\right)}\:{dx} \\ $$

Question Number 64993 Answers: 0 Comments: 0

let f(a) =∫_0 ^∞ ((cos(x^2 )−sin(x^2 ))/((x^2 +a^2 )^2 ))dx with a>0 1) calculate f(a) 2) find the values of ∫_0 ^∞ ((cos(x^2 )−sin(x^2 ))/((x^2 +1)^2 )) and ∫_0 ^∞ ((cos(x^2 )−sin(x^2 ))/((x^2 +3)^2 ))dx .

$${let}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({x}^{\mathrm{2}} \right)−{sin}\left({x}^{\mathrm{2}} \right)}{\left({x}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx}\:\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{values}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{cos}\left({x}^{\mathrm{2}} \right)−{sin}\left({x}^{\mathrm{2}} \right)}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} }\:{and} \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({x}^{\mathrm{2}} \right)−{sin}\left({x}^{\mathrm{2}} \right)}{\left({x}^{\mathrm{2}} \:+\mathrm{3}\right)^{\mathrm{2}} }{dx}\:. \\ $$

Question Number 64984 Answers: 1 Comments: 2

∫_0 ^3 x ∣x^2 − x − 2∣ dx = ?

$$\underset{\mathrm{0}} {\int}\:\overset{\mathrm{3}} {\:}\:{x}\:\mid{x}^{\mathrm{2}} \:−\:{x}\:−\:\mathrm{2}\mid\:{dx}\:\:=\:\:? \\ $$

Question Number 64975 Answers: 0 Comments: 1

Question Number 64973 Answers: 1 Comments: 0

Question Number 64971 Answers: 0 Comments: 3

Question Number 64970 Answers: 0 Comments: 9

let f(a)=∫_0 ^∞ ((cos(x^2 ) +sin(x^2 ))/((x^2 +a^2 )^2 )) dx with a>0 1) calculate f(a) 2) find the values of ∫_0 ^∞ ((cos(x^2 )+sin(x^2 ))/((x^2 +1)^2 ))dx and ∫_0 ^∞ ((cos(x^2 )+sin(x^2 ))/((x^2 +3)^2 ))dx

$${let}\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({x}^{\mathrm{2}} \right)\:+{sin}\left({x}^{\mathrm{2}} \right)}{\left({x}^{\mathrm{2}} \:+{a}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{dx}\:\:\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{values}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({x}^{\mathrm{2}} \right)+{sin}\left({x}^{\mathrm{2}} \right)}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }{dx}\:{and} \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\frac{{cos}\left({x}^{\mathrm{2}} \right)+{sin}\left({x}^{\mathrm{2}} \right)}{\left({x}^{\mathrm{2}} +\mathrm{3}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 64968 Answers: 0 Comments: 1

Question Number 64966 Answers: 0 Comments: 0

Question Number 64955 Answers: 0 Comments: 3

prove that Σ_(k=1) ^n k∙(((k+1)!)/2^(k+1) )=(((n+2)!)/2^(n+1) )−1

$${prove}\:{that}\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{k}\centerdot\frac{\left({k}+\mathrm{1}\right)!}{\mathrm{2}^{{k}+\mathrm{1}} }=\frac{\left({n}+\mathrm{2}\right)!}{\mathrm{2}^{{n}+\mathrm{1}} }−\mathrm{1} \\ $$

Question Number 64951 Answers: 1 Comments: 0

Question Number 64949 Answers: 1 Comments: 1

Question Number 64941 Answers: 0 Comments: 0

Question Number 64916 Answers: 1 Comments: 6

Question Number 64909 Answers: 1 Comments: 2

Question Number 64905 Answers: 0 Comments: 0

∫log (tan x)dx

$$\int\mathrm{log}\:\left(\mathrm{tan}\:\mathrm{x}\right)\mathrm{dx} \\ $$

Question Number 64904 Answers: 0 Comments: 2

calculate ∫_1 ^2 ∫_0 ^x (1/((x^2 +y^2 )^(3/2) ))dydx

$${calculate}\:\int_{\mathrm{1}} ^{\mathrm{2}} \:\int_{\mathrm{0}} ^{{x}} \:\:\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \right)^{\frac{\mathrm{3}}{\mathrm{2}}} }{dydx}\: \\ $$

Question Number 64903 Answers: 1 Comments: 2

1, 3, 7, 15, 30, 57, 103, x What′s x ?

$$\mathrm{1},\:\mathrm{3},\:\mathrm{7},\:\mathrm{15},\:\mathrm{30},\:\mathrm{57},\:\mathrm{103},\:{x} \\ $$$${What}'{s}\:\:{x}\:? \\ $$

Question Number 64901 Answers: 1 Comments: 11

Question Number 64895 Answers: 0 Comments: 0

Question Number 64894 Answers: 0 Comments: 0

Question Number 64893 Answers: 0 Comments: 0

Question Number 64892 Answers: 0 Comments: 0

Question Number 64887 Answers: 1 Comments: 0

Question Number 64886 Answers: 0 Comments: 0

let f(x) =cos((1/x)) 1) calculate f^((n)) (x) 2) developp f at integr serie at x_0 =(3/π)

$${let}\:{f}\left({x}\right)\:={cos}\left(\frac{\mathrm{1}}{{x}}\right)\:\:\: \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}\:{at}\:{x}_{\mathrm{0}} =\frac{\mathrm{3}}{\pi} \\ $$

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