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Question Number 66694 Answers: 0 Comments: 3

let f(a) =∫_(−∞) ^(+∞) (dx/((x^4 +x^2 +a))) with a∈](1/4),+∞[ 1) calculate f(a) 2)find also g(a) =∫_(−∞) ^(+∞) (dx/((x^4 +x^2 +a)^2 )) 3) find the value of integrals ∫_0 ^∞ (dx/((x^4 +x^2 +3))) and ∫_0 ^∞ (dx/((x^4 +x^2 +1)^2 )) 4) developp f at integrserie.

$$\left.{let}\:{f}\left({a}\right)\:=\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{\left({x}^{\mathrm{4}} +{x}^{\mathrm{2}} \:+{a}\right)}\:{with}\:{a}\in\right]\frac{\mathrm{1}}{\mathrm{4}},+\infty\left[\right. \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{also}\:{g}\left({a}\right)\:=\int_{−\infty} ^{+\infty} \:\frac{{dx}}{\left({x}^{\mathrm{4}} \:+{x}^{\mathrm{2}} +{a}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:{integrals}\:\:\int_{\mathrm{0}} ^{\infty} \:\frac{{dx}}{\left({x}^{\mathrm{4}} \:+{x}^{\mathrm{2}} \:+\mathrm{3}\right)}\:{and} \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{4}} \:+{x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{4}\right)\:{developp}\:{f}\:{at}\:{integrserie}. \\ $$

Question Number 66693 Answers: 1 Comments: 1

calculate ∫_(−∞) ^(+∞) (dx/((x^2 −x+1)^3 ))

$${calculate}\:\:\int_{−\infty} ^{+\infty} \:\frac{{dx}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)^{\mathrm{3}} } \\ $$

Question Number 66684 Answers: 1 Comments: 0

Question Number 66683 Answers: 1 Comments: 2

Question Number 66680 Answers: 0 Comments: 2

calculate Σ_(n=1) ^∞ (2^n /(3^n (2n^3 +n^2 −5n +2)))

$${calculate}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\:\frac{\mathrm{2}^{{n}} }{\mathrm{3}^{{n}} \left(\mathrm{2}{n}^{\mathrm{3}} \:+{n}^{\mathrm{2}} −\mathrm{5}{n}\:+\mathrm{2}\right)} \\ $$

Question Number 66670 Answers: 1 Comments: 1

Question Number 66667 Answers: 1 Comments: 3

Question Number 66664 Answers: 0 Comments: 0

Question Number 66656 Answers: 1 Comments: 1

Question Number 66640 Answers: 0 Comments: 6

lim_(x→4) ((((2+x(√x)))^(1/3) −2)/(8−x(√x)))=?

$$\: \\ $$$$\:\underset{\boldsymbol{{x}}\rightarrow\mathrm{4}} {\boldsymbol{{lim}}}\:\frac{\sqrt[{\mathrm{3}}]{\mathrm{2}+\boldsymbol{{x}}\sqrt{\boldsymbol{{x}}}}−\mathrm{2}}{\mathrm{8}−\boldsymbol{{x}}\sqrt{\boldsymbol{{x}}}}=? \\ $$$$\: \\ $$

Question Number 66629 Answers: 0 Comments: 1

Question Number 66627 Answers: 1 Comments: 4

Question Number 66621 Answers: 0 Comments: 7

Question Number 66620 Answers: 0 Comments: 3

find lim_(n→∞) I_n I_n =∫_0 ^∞ (dx/((1+coth (nx))^n )) ,n≥1

$${find}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{I}_{{n}} \\ $$$${I}_{{n}} =\int_{\mathrm{0}} ^{\infty} \frac{{dx}}{\left(\mathrm{1}+\mathrm{coth}\:\left({nx}\right)\right)^{{n}} }\:,{n}\geqslant\mathrm{1} \\ $$$$ \\ $$

Question Number 66619 Answers: 1 Comments: 0

solve for x,y∈R ((√(1+x^2 ))/(ln (x+(√(1+x^2 )))))=((√(1+y^2 ))/(ln (y+(√(1+y^2 )))))

$${solve}\:{for}\:{x},{y}\in{R} \\ $$$$\frac{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{\mathrm{ln}\:\left({x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right)}=\frac{\sqrt{\mathrm{1}+{y}^{\mathrm{2}} }}{\mathrm{ln}\:\left({y}+\sqrt{\mathrm{1}+{y}^{\mathrm{2}} }\right)} \\ $$

Question Number 66602 Answers: 2 Comments: 3

Question Number 66601 Answers: 1 Comments: 1

Question Number 66599 Answers: 0 Comments: 2

Question Number 66589 Answers: 2 Comments: 5

∫((sinx)/(1+sinx+sin2x))dx

$$\int\frac{{sinx}}{\mathrm{1}+{sinx}+{sin}\mathrm{2}{x}}{dx} \\ $$

Question Number 66564 Answers: 0 Comments: 0

Question Number 66561 Answers: 1 Comments: 2

evaluate ∫_0 ^2 ∣ x+ 2∣ dx.

$${evaluate}\: \\ $$$$\:\:\int_{\mathrm{0}} ^{\mathrm{2}} \mid\:{x}+\:\mathrm{2}\mid\:{dx}. \\ $$

Question Number 66562 Answers: 1 Comments: 1

given that ∣z − i∣ = ∣z − 4 +3 i∣ sketch the locus of z find the catersian equation of this locus.

$${given}\:{that}\:\:\mid{z}\:−\:\mathrm{i}\mid\:=\:\mid{z}\:−\:\mathrm{4}\:+\mathrm{3}\:\mathrm{i}\mid \\ $$$${sketch}\:{the}\:{locus}\:{of}\:\:{z} \\ $$$${find}\:{the}\:{catersian}\:{equation}\:{of}\:{this}\:{locus}. \\ $$

Question Number 66550 Answers: 0 Comments: 2

∫_0 ^1 ∫_((y/2) ) ^((1/2) ) e^(−x^2 ) dxdy=?

$$\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\frac{{y}}{\mathrm{2}}\:} ^{\frac{\mathrm{1}}{\mathrm{2}}\:} {e}^{−{x}^{\mathrm{2}} } {dxdy}=? \\ $$

Question Number 66549 Answers: 0 Comments: 0

((n^2 !)/((n!)^n ))=natural number.

$$\frac{\mathrm{n}^{\mathrm{2}} !}{\left(\mathrm{n}!\right)^{\mathrm{n}} }=\mathrm{natural}\:\mathrm{number}. \\ $$

Question Number 66548 Answers: 0 Comments: 1

Evaluate:∫(√(x(√(x+1)) ))dx

$$\boldsymbol{{Evaluate}}:\int\sqrt{{x}\sqrt{{x}+\mathrm{1}}\:}{dx} \\ $$

Question Number 66546 Answers: 0 Comments: 6

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