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Question Number 143320 Answers: 3 Comments: 0

prove that: tan^2 36° + tan^2 72° = 5

$${prove}\:{that}:\:\:{tan}^{\mathrm{2}} \mathrm{36}°\:+\:{tan}^{\mathrm{2}} \mathrm{72}°\:=\:\mathrm{5} \\ $$

Question Number 143317 Answers: 0 Comments: 1

Question Number 143312 Answers: 1 Comments: 0

∫_0 ^∞ ((sin^4 x)/x^4 )dx=(π/3)

$$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{sin}^{\mathrm{4}} \mathrm{x}}{\mathrm{x}^{\mathrm{4}} }\mathrm{dx}=\frac{\pi}{\mathrm{3}} \\ $$

Question Number 143296 Answers: 3 Comments: 0

Montrer que Γ(n)=(n−1)!

$${Montrer}\:{que} \\ $$$$\Gamma\left({n}\right)=\left({n}−\mathrm{1}\right)! \\ $$$$ \\ $$

Question Number 143293 Answers: 2 Comments: 0

f(x)=ln(1+ln(x)). f(x)=ln(f′(x)).Find x

$${f}\left({x}\right)={ln}\left(\mathrm{1}+{ln}\left({x}\right)\right). \\ $$$${f}\left({x}\right)={ln}\left({f}'\left({x}\right)\right).{Find}\:{x} \\ $$

Question Number 143287 Answers: 2 Comments: 0

Question Number 143284 Answers: 1 Comments: 0

Question Number 143274 Answers: 3 Comments: 0

Question Number 143270 Answers: 1 Comments: 0

Question Number 143268 Answers: 2 Comments: 0

lim_(x→∞) (((x+3)/(x−4)))^(−2) =?

$${li}\underset{{x}\rightarrow\infty} {{m}}\left(\frac{{x}+\mathrm{3}}{{x}−\mathrm{4}}\right)^{−\mathrm{2}} =? \\ $$

Question Number 143262 Answers: 1 Comments: 0

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

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

Question Number 143261 Answers: 1 Comments: 0

find Y_n =∫_0 ^∞ (dx/((x+1)(x+2)....(x+n))) (n>1 integr)

$${find}\:{Y}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)....\left({x}+{n}\right)} \\ $$$$\left({n}>\mathrm{1}\:{integr}\right) \\ $$

Question Number 143260 Answers: 0 Comments: 1

find ∫ (dx/( (√x)+(√(x+1))+(√(x+2))))

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

Question Number 143259 Answers: 1 Comments: 0

solve y^(′′) −y^′ +2=xsin(3x)

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

Question Number 143258 Answers: 1 Comments: 0

calculate lim_(x→1) ∫_x ^x^2 ((sh(xt))/(x+t))dt

$${calculate}\:{lim}_{{x}\rightarrow\mathrm{1}} \int_{{x}} ^{{x}^{\mathrm{2}} } \:\frac{{sh}\left({xt}\right)}{{x}+{t}}{dt} \\ $$

Question Number 143257 Answers: 0 Comments: 0

find ∫∫_([0,1]) e^(−(x^2 +y^2 )) arctan(2(√(x^2 +y^2 )))dxdy

$${find}\:\int\int_{\left[\mathrm{0},\mathrm{1}\right]} {e}^{−\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)} {arctan}\left(\mathrm{2}\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\right){dxdy} \\ $$

Question Number 143256 Answers: 0 Comments: 0

calculate ∫_0 ^1 ∫_x ^(2−x) e^(−xy) (√(x+y))dy dx

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \int_{{x}} ^{\mathrm{2}−{x}} {e}^{−{xy}} \sqrt{{x}+{y}}{dy}\:{dx} \\ $$

Question Number 143255 Answers: 2 Comments: 0

find lim_(x→0) ((sin(1−cosx)+1−cos(sinx))/x^2 )

$${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \frac{{sin}\left(\mathrm{1}−{cosx}\right)+\mathrm{1}−{cos}\left({sinx}\right)}{{x}^{\mathrm{2}} } \\ $$

Question Number 143254 Answers: 1 Comments: 0

find the value of Σ_(n=1) ^∞ (((−1)^n )/(n^2 (n+1)(n+2)(n+3)))

$${find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)\left({n}+\mathrm{3}\right)} \\ $$

Question Number 143253 Answers: 0 Comments: 0

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

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

Question Number 143252 Answers: 1 Comments: 0

lim_(x→0) ((8x−6x sin x+sin 2x)/x^5 ) =?

$$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{8}{x}−\mathrm{6}{x}\:\mathrm{sin}\:{x}+\mathrm{sin}\:\mathrm{2}{x}}{{x}^{\mathrm{5}} }\:=? \\ $$

Question Number 143251 Answers: 4 Comments: 0

Question Number 143248 Answers: 1 Comments: 1

∫(dx/(x^2 −4x+1))

$$\int\frac{{dx}}{{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{1}} \\ $$

Question Number 143240 Answers: 1 Comments: 0

(2/y)=(1/x)((a/y)+1) x=2(4a−y) Is equations system

$$\frac{\mathrm{2}}{{y}}=\frac{\mathrm{1}}{{x}}\left(\frac{{a}}{{y}}+\mathrm{1}\right) \\ $$$${x}=\mathrm{2}\left(\mathrm{4}{a}−{y}\right) \\ $$$${Is}\:{equations}\:{system} \\ $$

Question Number 143239 Answers: 0 Comments: 0

Question Number 143238 Answers: 1 Comments: 0

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