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Question Number 135419 Answers: 1 Comments: 0

(√3) tan x.cot x +(√3) tan x−cot x−1 = 0

$$\sqrt{\mathrm{3}}\:\mathrm{tan}\:{x}.\mathrm{cot}\:{x}\:+\sqrt{\mathrm{3}}\:\mathrm{tan}\:{x}−\mathrm{cot}\:{x}−\mathrm{1}\:=\:\mathrm{0} \\ $$

Question Number 135418 Answers: 2 Comments: 0

Given x+(1/x) = 5 then ((x^4 +(1/x^4 ))/(x^2 −3x+1)) ?

$${Given}\:{x}+\frac{\mathrm{1}}{{x}}\:=\:\mathrm{5}\:{then}\:\frac{{x}^{\mathrm{4}} +\frac{\mathrm{1}}{{x}^{\mathrm{4}} }}{{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{1}}\:? \\ $$

Question Number 135415 Answers: 3 Comments: 1

Question Number 135413 Answers: 0 Comments: 1

Question Number 135405 Answers: 0 Comments: 2

Question Number 135402 Answers: 1 Comments: 0

Question Number 135401 Answers: 0 Comments: 0

find integrating factor or this diff. equ^n for which it become exact (x^2 −xy−y^2 )dy+y^2 dx=0

$${find}\:{integrating}\:{factor}\:{or}\:{this}\:{diff}. \\ $$$${equ}^{{n}} \:{for}\:{which}\:{it}\:{become}\:{exact}\: \\ $$$$\left({x}^{\mathrm{2}} −{xy}−{y}^{\mathrm{2}} \right){dy}+{y}^{\mathrm{2}} {dx}=\mathrm{0} \\ $$

Question Number 135395 Answers: 6 Comments: 0

Question Number 135393 Answers: 1 Comments: 0

f ′(x)=(((x−3)^3 (x^2 −4))/(16)) g(x)=f(x^2 −1) find g′(2)

$${f}\:'\left({x}\right)=\frac{\left({x}−\mathrm{3}\right)^{\mathrm{3}} \left({x}^{\mathrm{2}} −\mathrm{4}\right)}{\mathrm{16}} \\ $$$${g}\left({x}\right)={f}\left({x}^{\mathrm{2}} −\mathrm{1}\right) \\ $$$${find}\:{g}'\left(\mathrm{2}\right) \\ $$

Question Number 135389 Answers: 0 Comments: 0

let U_n =∫_(−∞) ^∞ ((cos(nx))/((x^2 −x+1)^2 ))dx calculate lim_(n→∞) e^n^2 U_n

$${let}\:{U}_{{n}} =\int_{−\infty} ^{\infty} \:\:\frac{{cos}\left({nx}\right)}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$$${calculate}\:{lim}_{{n}\rightarrow\infty} {e}^{{n}^{\mathrm{2}} } {U}_{{n}} \\ $$

Question Number 135388 Answers: 1 Comments: 0

find lim_(n→∞) ∫_(1/n) ^(1+(1/n)) Γ(x).Γ(1−x)dx

$${find}\:\:{lim}_{{n}\rightarrow\infty} \int_{\frac{\mathrm{1}}{{n}}} ^{\mathrm{1}+\frac{\mathrm{1}}{{n}}} \Gamma\left({x}\right).\Gamma\left(\mathrm{1}−{x}\right){dx} \\ $$

Question Number 135385 Answers: 0 Comments: 0

1−(1/2) (1/x^2 )+(1/2)(3/4) (1/x^4 )−(1/2)(3/4)(5/6) (1/x^6 )+....=?

$$\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{2}}\frac{\mathrm{3}}{\mathrm{4}}\:\frac{\mathrm{1}}{{x}^{\mathrm{4}} }−\frac{\mathrm{1}}{\mathrm{2}}\frac{\mathrm{3}}{\mathrm{4}}\frac{\mathrm{5}}{\mathrm{6}}\:\frac{\mathrm{1}}{{x}^{\mathrm{6}} }+....=? \\ $$

Question Number 135384 Answers: 3 Comments: 0

let f(x)=ln(2+x^3 ) if f(x)=Σa_n x^n find a_n

$${let}\:{f}\left({x}\right)={ln}\left(\mathrm{2}+{x}^{\mathrm{3}} \right) \\ $$$${if}\:{f}\left({x}\right)=\Sigma{a}_{{n}} {x}^{{n}} \\ $$$${find}\:{a}_{{n}} \\ $$

Question Number 135382 Answers: 1 Comments: 0

find ∫_0 ^1 x^n ln(1−x^4 )dx with n integr natural

$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{{n}} {ln}\left(\mathrm{1}−{x}^{\mathrm{4}} \right){dx}\:{with}\:{n} \\ $$$${integr}\:{natural} \\ $$

Question Number 135381 Answers: 0 Comments: 0

let Φ(x)=ln(sinx −cosx) developp Φ at fourier serie

$${let}\:\Phi\left({x}\right)={ln}\left({sinx}\:−{cosx}\right) \\ $$$${developp}\:\Phi\:{at}\:{fourier}\:{serie} \\ $$

Question Number 135380 Answers: 0 Comments: 0

calculate ∫_0 ^∞ e^(−x) ln(1+x^2 )dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{x}} {ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right){dx} \\ $$

Question Number 135378 Answers: 1 Comments: 0

compare without calculator 5((√(1+(√7)))−1) and 7((√(1+(√5)))−1)

$${compare}\:{without}\:{calculator} \\ $$$$\mathrm{5}\left(\sqrt{\mathrm{1}+\sqrt{\mathrm{7}}}−\mathrm{1}\right)\:{and}\:\mathrm{7}\left(\sqrt{\mathrm{1}+\sqrt{\mathrm{5}}}−\mathrm{1}\right) \\ $$

Question Number 135377 Answers: 0 Comments: 0

solve x^2 y^(′′) +(1+x^2 )y^′ +3y =e^(−x)

$${solve}\:{x}^{\mathrm{2}} {y}^{''} +\left(\mathrm{1}+{x}^{\mathrm{2}} \right){y}^{'} \:+\mathrm{3}{y}\:={e}^{−{x}} \\ $$

Question Number 135376 Answers: 0 Comments: 0

solve y^(′′ ) =1+(y/x)+(y^2 /x^2 )

$${solve}\:{y}^{''\:} =\mathrm{1}+\frac{{y}}{{x}}+\frac{{y}^{\mathrm{2}} }{{x}^{\mathrm{2}} } \\ $$

Question Number 135375 Answers: 0 Comments: 0

let ϕ(x)=((arctan(x))/(x^2 +3)) developp ϕ at integr serie

$${let}\:\varphi\left({x}\right)=\frac{{arctan}\left({x}\right)}{{x}^{\mathrm{2}} +\mathrm{3}} \\ $$$${developp}\:\varphi\:{at}\:{integr}\:{serie} \\ $$

Question Number 135373 Answers: 0 Comments: 0

determine the sequence u_n wich verify u_n +u_(n+1) =(((−1)^n )/(n!))

$${determine}\:{the}\:{sequence}\:{u}_{{n}} \\ $$$${wich}\:{verify}\:{u}_{{n}} \:+{u}_{{n}+\mathrm{1}} =\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}!} \\ $$

Question Number 135372 Answers: 0 Comments: 0

calculate ∫_0 ^∞ (dx/(((√x)+(√(1+x^2 )))^3 ))

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

Question Number 135370 Answers: 0 Comments: 0

let f(x)=(1/(cosx +2sinx)) developp f at fourier serie

$${let}\:{f}\left({x}\right)=\frac{\mathrm{1}}{{cosx}\:+\mathrm{2}{sinx}} \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{serie} \\ $$

Question Number 135369 Answers: 0 Comments: 0

let f(x)=e^(−2x) ln(3+x) 1) calculate f^((n) )(x) and f^((n)) (0) 2)developp f at integr serie

$${let}\:{f}\left({x}\right)={e}^{−\mathrm{2}{x}} {ln}\left(\mathrm{3}+{x}\right) \\ $$$$\left.\mathrm{1}\left.\right)\:{calculate}\:{f}^{\left({n}\right.} \right)\left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right){developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$

Question Number 135368 Answers: 1 Comments: 0

calculate ∫_0 ^(+∞) ((xarctan(2x))/((x^2 +1)^2 ))dx

$${calculate}\:\int_{\mathrm{0}} ^{+\infty} \:\:\frac{{xarctan}\left(\mathrm{2}{x}\right)}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 135366 Answers: 1 Comments: 0

∫_0 ^1 (1/( ((6x−15x^2 +20x^3 −15x^4 +6x^5 −x^6 ))^(1/6) ))dx=(π/3) Or ∫_0 ^1 (1/( ((kx−((k(k−1))/2)x^2 +((k(k−1)(k−2))/6)x^3 −...))^(1/k) ))dx=(π/(ksin((π/k))))

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\:\sqrt[{\mathrm{6}}]{\mathrm{6}{x}−\mathrm{15}{x}^{\mathrm{2}} +\mathrm{20}{x}^{\mathrm{3}} −\mathrm{15}{x}^{\mathrm{4}} +\mathrm{6}{x}^{\mathrm{5}} −{x}^{\mathrm{6}} }}{dx}=\frac{\pi}{\mathrm{3}} \\ $$$${Or} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\:\sqrt[{{k}}]{{kx}−\frac{{k}\left({k}−\mathrm{1}\right)}{\mathrm{2}}{x}^{\mathrm{2}} +\frac{{k}\left({k}−\mathrm{1}\right)\left({k}−\mathrm{2}\right)}{\mathrm{6}}{x}^{\mathrm{3}} −...}}{dx}=\frac{\pi}{{ksin}\left(\frac{\pi}{{k}}\right)} \\ $$

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