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AllQuestion and Answers: Page 1512

Question Number 60340 Answers: 0 Comments: 0

Question Number 60337 Answers: 0 Comments: 2

15,25,42,...?

$$\mathrm{15},\mathrm{25},\mathrm{42},...? \\ $$

Question Number 60335 Answers: 0 Comments: 0

find I_n = ∫ x^n arctan(x)dx with n integr natural.

$${find}\:{I}_{{n}} =\:\int\:\:{x}^{{n}} \:{arctan}\left({x}\right){dx}\:\:{with}\:{n}\:{integr}\:{natural}. \\ $$

Question Number 60330 Answers: 0 Comments: 1

Question Number 60354 Answers: 0 Comments: 0

Question Number 60351 Answers: 0 Comments: 2

Question Number 60357 Answers: 0 Comments: 1

Question Number 60347 Answers: 1 Comments: 1

Question Number 60346 Answers: 0 Comments: 1

∫xsec^3 xdx please help

$$\int{x}\mathrm{sec}\:^{\mathrm{3}} {xdx} \\ $$$${please}\:{help} \\ $$

Question Number 60322 Answers: 1 Comments: 2

Question Number 60321 Answers: 0 Comments: 2

Question Number 60320 Answers: 0 Comments: 1

Question Number 60319 Answers: 0 Comments: 0

Question Number 60318 Answers: 0 Comments: 2

Question Number 60439 Answers: 2 Comments: 1

Question Number 60313 Answers: 3 Comments: 1

Question Number 60311 Answers: 1 Comments: 2

∫(dx/(√(sec h^2 (x)+1))) dx

$$\int\frac{{dx}}{\sqrt{{sec}\:{h}^{\mathrm{2}} \left({x}\right)+\mathrm{1}}}\:{dx} \\ $$

Question Number 60308 Answers: 0 Comments: 0

Question Number 60307 Answers: 0 Comments: 0

Question Number 60304 Answers: 0 Comments: 0

Question Number 60303 Answers: 1 Comments: 0

Question Number 60287 Answers: 2 Comments: 2

f(x) = x^3 + 3x − 7 f^(−1) (x) = ?

$${f}\left({x}\right)\:\:=\:\:{x}^{\mathrm{3}} \:+\:\mathrm{3}{x}\:−\:\mathrm{7} \\ $$$${f}\:^{−\mathrm{1}} \left({x}\right)\:\:=\:\:? \\ $$

Question Number 60283 Answers: 1 Comments: 1

Question Number 60269 Answers: 3 Comments: 3

if tan A − cot A = 0 prove that sin A + cos A=?

$${if} \\ $$$${tan}\:{A}\:−\:{cot}\:{A}\:=\:\mathrm{0} \\ $$$${prove}\:{that} \\ $$$${sin}\:{A}\:+\:{cos}\:{A}=? \\ $$

Question Number 60264 Answers: 0 Comments: 0

let f(t) =∫_0 ^∞ (e^(−3 [x^2 ]) /(x^2 +t^2 ))dx with t>0 1. determine a explicit form of f(t) 2. find also g(t) =∫_0 ^∞ (e^(−3[x^2 ]) /((x^2 +t^2 )^2 ))dx 3. find the values of integrals ∫_0 ^∞ (e^(−3[x^2 ]) /(x^2 +3))dx and ∫_0 ^∞ (e^(−3[x^2 ]) /((x^2 +4)^2 )) dx .

$${let}\:{f}\left({t}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{e}^{−\mathrm{3}\:\left[{x}^{\mathrm{2}} \right]} }{{x}^{\mathrm{2}} \:+{t}^{\mathrm{2}} }{dx}\:\:{with}\:{t}>\mathrm{0} \\ $$$$\mathrm{1}.\:{determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({t}\right) \\ $$$$\mathrm{2}.\:{find}\:{also}\:{g}\left({t}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−\mathrm{3}\left[{x}^{\mathrm{2}} \right]} }{\left({x}^{\mathrm{2}} \:+{t}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx} \\ $$$$\mathrm{3}.\:{find}\:{the}\:{values}\:{of}\:{integrals}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{e}^{−\mathrm{3}\left[{x}^{\mathrm{2}} \right]} }{{x}^{\mathrm{2}} \:+\mathrm{3}}{dx}\:\:{and}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−\mathrm{3}\left[{x}^{\mathrm{2}} \right]} }{\left({x}^{\mathrm{2}} \:+\mathrm{4}\right)^{\mathrm{2}} }\:{dx}\:. \\ $$

Question Number 60263 Answers: 0 Comments: 1

let U_n =∫_0 ^∞ (e^(−n[x^2 ]) /(x^2 +3)) dx 1) calculate U_n interms of n 2) find lim_(n→+∞) n U_n 3)determine nature of the serie Σ U_n

$${let}\:{U}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{e}^{−{n}\left[{x}^{\mathrm{2}} \right]} }{{x}^{\mathrm{2}} +\mathrm{3}}\:{dx}\: \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{U}_{{n}} \:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{n}\:{U}_{{n}} \\ $$$$\left.\mathrm{3}\right){determine}\:{nature}\:{of}\:{the}\:{serie}\:\:\Sigma\:{U}_{{n}} \\ $$

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