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Question Number 73490    Answers: 0   Comments: 0

calculate f(a) =∫_0 ^∞ e^(−(x^2 +(a/x^2 ))) dx with a>0

$${calculate}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−\left({x}^{\mathrm{2}} \:+\frac{{a}}{{x}^{\mathrm{2}} }\right)} {dx}\:\:{with}\:{a}>\mathrm{0} \\ $$

Question Number 73489    Answers: 0   Comments: 0

calculate ∫_0 ^∞ ((arctan(3+x^2 ))/((2 x^2 +9)^2 ))dx

$${calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{arctan}\left(\mathrm{3}+{x}^{\mathrm{2}} \right)}{\left(\mathrm{2}\:{x}^{\mathrm{2}} +\mathrm{9}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 73488    Answers: 2   Comments: 1

solve xy^(′′) +(x^2 −1)y^′ =x e^(−x^2 )

$${solve}\:\:\:{xy}^{''} \:\:+\left({x}^{\mathrm{2}} −\mathrm{1}\right){y}^{'} \:\:={x}\:{e}^{−{x}^{\mathrm{2}} } \\ $$

Question Number 73487    Answers: 0   Comments: 1

let α and β roots of the equation x^2 −x+2=0 simplify A_p = α^p +β^p and calculate Σ_(p=0) ^(n−1) A_p and Σ_(p=0) ^(n−1) A_p ^2

$${let}\:\:\:\:\alpha\:{and}\:\beta\:{roots}\:{of}\:\:{the}\:{equation}\:\:{x}^{\mathrm{2}} −{x}+\mathrm{2}=\mathrm{0} \\ $$$${simplify}\:\:\:{A}_{{p}} =\:\alpha^{{p}} \:+\beta^{{p}} \:{and}\:{calculate} \\ $$$$\sum_{{p}=\mathrm{0}} ^{{n}−\mathrm{1}} \:{A}_{{p}} \:\:{and}\:\sum_{{p}=\mathrm{0}} ^{{n}−\mathrm{1}} \:\:{A}_{{p}} ^{\mathrm{2}} \\ $$

Question Number 73486    Answers: 0   Comments: 2

let P(x)=(1+ix)^n −(1−ix)^n with n integr decompose the Fraction F (x)=(1/(P(x)))

$${let}\:{P}\left({x}\right)=\left(\mathrm{1}+{ix}\right)^{{n}} −\left(\mathrm{1}−{ix}\right)^{{n}} \:{with}\:{n}\:{integr} \\ $$$${decompose}\:{the}\:{Fraction}\:{F}\:\left({x}\right)=\frac{\mathrm{1}}{{P}\left({x}\right)} \\ $$

Question Number 73485    Answers: 0   Comments: 0

find the roots of P(x)=(1+ix +jx^2 )^n −1 with j =e^(i((2π)/3)) then factorize P(x) inside C[x] decompose the fraction F=(1/P)

$${find}\:{the}\:{roots}\:{of}\:{P}\left({x}\right)=\left(\mathrm{1}+{ix}\:+{jx}^{\mathrm{2}} \right)^{{n}} −\mathrm{1} \\ $$$${with}\:{j}\:={e}^{{i}\frac{\mathrm{2}\pi}{\mathrm{3}}} \:\:\:{then}\:{factorize}\:{P}\left({x}\right)\:{inside}\:{C}\left[{x}\right] \\ $$$${decompose}\:{the}\:{fraction}\:{F}=\frac{\mathrm{1}}{{P}} \\ $$

Question Number 73484    Answers: 1   Comments: 0

decompose inside C(x) the fraction F(x)=(1/((x^2 +1)^n )) calculate ∫_0 ^∞ F(x)dx

$${decompose}\:{inside}\:{C}\left({x}\right)\:{the}\:{fraction} \\ $$$${F}\left({x}\right)=\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{{n}} } \\ $$$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:{F}\left({x}\right){dx} \\ $$

Question Number 73483    Answers: 1   Comments: 0

find ∫ (dx/(x+2−(√(x^2 −x +7))))

$${find}\:\int\:\:\:\:\frac{{dx}}{{x}+\mathrm{2}−\sqrt{{x}^{\mathrm{2}} −{x}\:+\mathrm{7}}} \\ $$

Question Number 73482    Answers: 1   Comments: 1

find ∫ (dx/((√(x^2 +1))+(√(x^2 +3))))

$${find}\:\int\:\:\:\:\frac{{dx}}{\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}+\sqrt{{x}^{\mathrm{2}} \:+\mathrm{3}}} \\ $$

Question Number 73481    Answers: 0   Comments: 0

find ∫ ln(x−cosx)dx

$${find}\:\int\:\:{ln}\left({x}−{cosx}\right){dx} \\ $$

Question Number 73480    Answers: 0   Comments: 0

find ∫_0 ^∞ xe^(−x^2 ) arcran(x+(1/x))dx

$${find}\:\int_{\mathrm{0}} ^{\infty} \:\:{xe}^{−{x}^{\mathrm{2}} } \:{arcran}\left({x}+\frac{\mathrm{1}}{{x}}\right){dx} \\ $$

Question Number 73479    Answers: 1   Comments: 1

find ∫ ((3x+2)/((x+1)^2 (x−2)^3 ))dx

$${find}\:\int\:\:\:\:\frac{\mathrm{3}{x}+\mathrm{2}}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} \left({x}−\mathrm{2}\right)^{\mathrm{3}} }{dx} \\ $$

Question Number 73478    Answers: 1   Comments: 0

find ∫_0 ^1 ((x^3 −3)/(√(x^2 −x +2)))dx

$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\:\frac{{x}^{\mathrm{3}} −\mathrm{3}}{\sqrt{{x}^{\mathrm{2}} −{x}\:+\mathrm{2}}}{dx} \\ $$

Question Number 73477    Answers: 1   Comments: 0

calculate ∫ ((x^3 −4x+5)/(x^2 −x +1))dx

$${calculate}\:\int\:\:\:\frac{{x}^{\mathrm{3}} −\mathrm{4}{x}+\mathrm{5}}{{x}^{\mathrm{2}} −{x}\:+\mathrm{1}}{dx} \\ $$

Question Number 73474    Answers: 0   Comments: 0

⌉888>>>>>>>

$$\rceil\mathrm{888}>>>>>>> \\ $$

Question Number 73473    Answers: 0   Comments: 1

let z from C prove that arcsinz=−iln(iz+(√(1−z^2 ))) arccosz =−iln(z+(√(z^2 −1)))

$${let}\:{z}\:{from}\:{C}\:{prove}\:{that}\: \\ $$$${arcsinz}=−{iln}\left({iz}+\sqrt{\mathrm{1}−{z}^{\mathrm{2}} }\right) \\ $$$${arccosz}\:=−{iln}\left({z}+\sqrt{{z}^{\mathrm{2}} −\mathrm{1}}\right) \\ $$

Question Number 73468    Answers: 1   Comments: 0

soit le systeme suivant { ((2s+4c+3t=700)),((3s+2c+2t=500)) :} 8s+7c+8t=...?... comment determiner le resultat ...?... de la 3^e equation ?

$$\mathrm{soit}\:\mathrm{le}\:\mathrm{systeme}\:\mathrm{suivant} \\ $$$$\begin{cases}{\mathrm{2s}+\mathrm{4c}+\mathrm{3t}=\mathrm{700}}\\{\mathrm{3s}+\mathrm{2c}+\mathrm{2t}=\mathrm{500}}\end{cases} \\ $$$$\:\:\mathrm{8s}+\mathrm{7c}+\mathrm{8t}=...?... \\ $$$$\mathrm{comment}\:\mathrm{determiner}\:\mathrm{le}\:\mathrm{resultat}\:...?...\: \\ $$$$\mathrm{de}\:\mathrm{la}\:\mathrm{3}^{\mathrm{e}} \mathrm{equation}\:? \\ $$

Question Number 73466    Answers: 1   Comments: 0

please explain this Lim_(x→0) ((sinx)/x) = 1 by l′hopitals theorem Lim_(x→0) ((sinx)/x) = 0 by Squeez theorem is there something wrong?

$${please}\:{explain}\:{this}\: \\ $$$$\:\underset{{x}\rightarrow\mathrm{0}} {{Lim}}\frac{{sinx}}{{x}}\:=\:\mathrm{1}\:\:{by}\:{l}'{hopitals}\:{theorem} \\ $$$$ \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {{Lim}}\:\frac{{sinx}}{{x}}\:=\:\mathrm{0}\:{by}\:{Squeez}\:{theorem} \\ $$$${is}\:{there}\:{something}\:{wrong}? \\ $$

Question Number 73451    Answers: 0   Comments: 3

Question Number 73441    Answers: 1   Comments: 0

Question Number 73428    Answers: 1   Comments: 2

Evaluate : 1) ∫_(−2) ^( 2) ∫_(−(√(4−x^2 ))) ^( (√(4−x^2 ))) (3−x)dydx . (after changing the integral to polar form). 2) ∫_0 ^4 ∫_0 ^(4−x) ∫_0 ^( 4−(y^2 /4)) dzdydx .

$${Evaluate}\:: \\ $$$$\left.\mathrm{1}\right)\:\int_{−\mathrm{2}} ^{\:\mathrm{2}} \int_{−\sqrt{\mathrm{4}−{x}^{\mathrm{2}} }} ^{\:\sqrt{\mathrm{4}−{x}^{\mathrm{2}} }} \:\left(\mathrm{3}−{x}\right){dydx}\:. \\ $$$$\left({after}\:{changing}\:{the}\:{integral}\:{to}\:{polar}\:{form}\right). \\ $$$$ \\ $$$$\left.\mathrm{2}\right)\:\int_{\mathrm{0}} ^{\mathrm{4}} \int_{\mathrm{0}} ^{\mathrm{4}−{x}} \int_{\mathrm{0}} ^{\:\mathrm{4}−\frac{{y}^{\mathrm{2}} }{\mathrm{4}}} \:{dzdydx}\:. \\ $$

Question Number 73429    Answers: 1   Comments: 3

Solve : ∫(([cos^(−1) x(√(1−x^2 ))]^(−1) )/(log_e [2+((sin(2x(√(1−x^2 ))))/π)]))dx Evaluate ∫_(−π/2) ^( π/2) sin^2 xcos^2 x(cosx+sinx)dx

$$\:\:\:{Solve}\::\:\int\frac{\left[{cos}^{−\mathrm{1}} {x}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\right]^{−\mathrm{1}} }{{log}_{{e}} \left[\mathrm{2}+\frac{{sin}\left(\mathrm{2}{x}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\right)}{\pi}\right]}{dx} \\ $$$$\:\:{Evaluate}\:\:\int_{−\pi/\mathrm{2}} ^{\:\pi/\mathrm{2}} {sin}^{\mathrm{2}} {xcos}^{\mathrm{2}} {x}\left({cosx}+{sinx}\right){dx} \\ $$

Question Number 73411    Answers: 2   Comments: 2

calculate 1)cos(1+i) , sin(1+3i) 2) arctan(i), arctan(2i) , arctan(1+i) ,arctan(1−i) , arctan(1+2i). 3) have us conj(arctanz)=arctan(z^− )?

$${calculate}\:\: \\ $$$$\left.\mathrm{1}\right){cos}\left(\mathrm{1}+{i}\right)\:,\:{sin}\left(\mathrm{1}+\mathrm{3}{i}\right) \\ $$$$\left.\mathrm{2}\right)\:{arctan}\left({i}\right),\:{arctan}\left(\mathrm{2}{i}\right)\:,\:{arctan}\left(\mathrm{1}+{i}\right)\:,{arctan}\left(\mathrm{1}−{i}\right)\:, \\ $$$${arctan}\left(\mathrm{1}+\mathrm{2}{i}\right). \\ $$$$\left.\mathrm{3}\right)\:{have}\:{us}\:\:{conj}\left({arctanz}\right)={arctan}\left(\overset{−} {{z}}\right)? \\ $$

Question Number 73406    Answers: 0   Comments: 0

Use the Sandwich( Pinchin or Squeez ) theorem to prove that Lim_(x→a) (√x) = (√a)

$${Use}\:{the}\:{Sandwich}\left(\:{Pinchin}\:{or}\:{Squeez}\:\right)\:{theorem}\:{to}\:{prove} \\ $$$${that}\: \\ $$$$\:\underset{{x}\rightarrow{a}} {\mathrm{Lim}}\:\sqrt{{x}}\:=\:\sqrt{{a}}\: \\ $$

Question Number 73405    Answers: 0   Comments: 0

can someone please prove the Chinese Remainder theorem, for modula arithmetic?

$${can}\:{someone}\:{please}\:{prove}\:{the}\: \\ $$$${Chinese}\:{Remainder}\:{theorem},\:{for}\: \\ $$$${modula}\:{arithmetic}? \\ $$

Question Number 73399    Answers: 3   Comments: 1

{ ((x^2 +y^2 =65)),(((x−1)(y−1)=17)) :} please help me to solve it...

$$\begin{cases}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{65}}\\{\left({x}−\mathrm{1}\right)\left({y}−\mathrm{1}\right)=\mathrm{17}}\end{cases} \\ $$$$ \\ $$$${please}\:{help}\:{me}\:{to}\:{solve}\:{it}... \\ $$

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