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Question Number 85807 Answers: 1 Comments: 0

∫_0 ^1 ((x^2 dx)/(√(1−x^4 )))

$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\mathrm{x}^{\mathrm{2}} \:\mathrm{dx}}{\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{4}} }} \\ $$

Question Number 85801 Answers: 0 Comments: 3

calculate ∫_0 ^π (dx/((cosx +2sinx)^2 ))

$${calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{{dx}}{\left({cosx}\:+\mathrm{2}{sinx}\right)^{\mathrm{2}} } \\ $$

Question Number 85793 Answers: 0 Comments: 0

∫_1 ^2 ((tan^(−1) (x−1) ln(x−1))/x) dx

$$\int_{\mathrm{1}} ^{\mathrm{2}} \frac{{tan}^{−\mathrm{1}} \left({x}−\mathrm{1}\right)\:{ln}\left({x}−\mathrm{1}\right)}{{x}}\:{dx} \\ $$

Question Number 85789 Answers: 1 Comments: 0

∫(ln x)^2 dx =

$$\int\left(\mathrm{ln}\:{x}\right)^{\mathrm{2}} \:{dx}\:= \\ $$

Question Number 85786 Answers: 0 Comments: 0

posons (1+2(√3))^n =a_n +b_n (√3) montre que pgcd(a_n ;b_n )=1

$${posons}\: \\ $$$$\left(\mathrm{1}+\mathrm{2}\sqrt{\mathrm{3}}\right)^{\boldsymbol{{n}}} =\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} +\boldsymbol{\mathrm{b}}_{\boldsymbol{\mathrm{n}}} \sqrt{\mathrm{3}} \\ $$$$\boldsymbol{\mathrm{montre}}\:\boldsymbol{\mathrm{que}}\:\boldsymbol{\mathrm{pgcd}}\left(\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} ;\boldsymbol{{b}}_{\boldsymbol{{n}}} \right)=\mathrm{1} \\ $$

Question Number 85781 Answers: 1 Comments: 2

∫_0 ^1 (ln (1/x))^(−3/2) dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \:\left(\mathrm{ln}\:\frac{\mathrm{1}}{{x}}\right)^{−\mathrm{3}/\mathrm{2}} \:{dx} \\ $$

Question Number 85779 Answers: 0 Comments: 0

Question Number 85776 Answers: 1 Comments: 0

Question Number 85775 Answers: 0 Comments: 0

Question Number 85774 Answers: 0 Comments: 0

(x_(2n) )=2^(2n) ((x/2))_n (((x+1)/2))_n (x)_(m n) =m^(m n) Π_(k=0) ^(m=1) (((x+k)/m))_n , m∈z now if m is relative number such as(3/2) , m∈Q (x)_((3/2)n) =?? help me

$$\left({x}_{\mathrm{2}{n}} \right)=\mathrm{2}^{\mathrm{2}{n}} \left(\frac{{x}}{\mathrm{2}}\right)_{{n}} \left(\frac{{x}+\mathrm{1}}{\mathrm{2}}\right)_{{n}} \\ $$$$\left({x}\right)_{{m}\:{n}} ={m}^{{m}\:{n}} \underset{{k}=\mathrm{0}} {\overset{{m}=\mathrm{1}} {\prod}}\left(\frac{{x}+{k}}{{m}}\right)_{{n}} \:\:\:,\:{m}\in{z} \\ $$$${now}\:{if}\:{m}\:{is}\:{relative}\:{number}\:{such}\:{as}\frac{\mathrm{3}}{\mathrm{2}}\:,\:{m}\in{Q} \\ $$$$\left({x}\right)_{\frac{\mathrm{3}}{\mathrm{2}}{n}} =?? \\ $$$$ \\ $$$${help}\:{me}\: \\ $$

Question Number 85766 Answers: 0 Comments: 2

(dy/dx) = 1−sin (x+2y)

$$\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{1}−\mathrm{sin}\:\left(\mathrm{x}+\mathrm{2y}\right) \\ $$

Question Number 85762 Answers: 0 Comments: 12

Question Number 85760 Answers: 0 Comments: 0

∫(([cos^(−1) (x){(√(1−x^2 ))}]^(−1) )/(log{((sin(2x(√(1−x^2 ))))/π)})) dx

$$\int\frac{\left[{cos}^{−\mathrm{1}} \left({x}\right)\left\{\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\right\}\right]^{−\mathrm{1}} }{{log}\left\{\frac{{sin}\left(\mathrm{2}{x}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\right)}{\pi}\right\}}\:{dx} \\ $$

Question Number 85756 Answers: 0 Comments: 5

Question Number 85739 Answers: 1 Comments: 0

If F (x)=∫_x^2 ^x^3 log t dt (x>0), then F ′(x)=

$$\mathrm{If}\:{F}\:\left({x}\right)=\underset{{x}^{\mathrm{2}} } {\overset{{x}^{\mathrm{3}} } {\int}}\:\mathrm{log}\:{t}\:{dt}\:\:\left({x}>\mathrm{0}\right),\:\mathrm{then}\:{F}\:'\left({x}\right)= \\ $$

Question Number 85729 Answers: 0 Comments: 6

if march 24, 2020 is Tuesday, then march 24, 2032 is the day ?

$$\mathrm{if}\:\mathrm{march}\:\mathrm{24},\:\mathrm{2020}\:\mathrm{is}\:\mathrm{Tuesday}, \\ $$$$\mathrm{then}\:\mathrm{march}\:\mathrm{24},\:\mathrm{2032}\:\mathrm{is}\:\mathrm{the}\:\mathrm{day}\:? \\ $$

Question Number 85721 Answers: 1 Comments: 0

show that ∫_0 ^∞ ((e^(−x) ln(x))/(√x))dx=−(√π)(γ+ln(4))

$${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{{e}^{−{x}} {ln}\left({x}\right)}{\sqrt{{x}}}{dx}=−\sqrt{\pi}\left(\gamma+{ln}\left(\mathrm{4}\right)\right) \\ $$

Question Number 85718 Answers: 1 Comments: 0

∫((sin(x)−cos(3x))/(sin(x)−cos(2x)))dx

$$\int\frac{{sin}\left({x}\right)−{cos}\left(\mathrm{3}{x}\right)}{{sin}\left({x}\right)−{cos}\left(\mathrm{2}{x}\right)}{dx} \\ $$

Question Number 85717 Answers: 1 Comments: 0

∫_0 ^2 x^4 (√(1−x^2 )) dx ∫_0 ^1 x^(10) (1−x^n )dx

$$\int_{\mathrm{0}} ^{\mathrm{2}} {x}^{\mathrm{4}} \sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\:{dx} \\ $$$$ \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{\mathrm{10}} \left(\mathrm{1}−{x}^{{n}} \right){dx} \\ $$$$ \\ $$

Question Number 85711 Answers: 0 Comments: 2

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

$$\:\underset{−\mathrm{4}} {\overset{\mathrm{2}} {\int}}\:\frac{\mathrm{2}{x}\:+\:\mathrm{1}}{\left({x}^{\mathrm{2}} +\:{x}\:+\:\mathrm{1}\right)^{\mathrm{3}/\mathrm{2}} }\:{dx} \\ $$

Question Number 85709 Answers: 1 Comments: 0

Question Number 85708 Answers: 1 Comments: 0

lim_(n−∞) /((U_n +1)/(Un))/ >0 Test for convergence

$${li}\underset{{n}−\infty} {{m}}\:\:/\frac{{U}_{{n}} +\mathrm{1}}{{Un}}/\:\:\:>\mathrm{0} \\ $$$${Test}\:{for}\:{convergence} \\ $$

Question Number 85706 Answers: 1 Comments: 0

Find the general solution of x^2 (√(y^2 +9)) dx + 5 (√(x^2 −3)) y dy = 0

$${Find}\:\:{the}\:\:{general}\:\:{solution}\:\:{of} \\ $$$$\:\:\:\:\:\:{x}^{\mathrm{2}} \:\sqrt{{y}^{\mathrm{2}} +\mathrm{9}}\:\:{dx}\:+\:\mathrm{5}\:\sqrt{{x}^{\mathrm{2}} −\mathrm{3}}\:\:{y}\:{dy}\:\:=\:\:\mathrm{0} \\ $$

Question Number 85701 Answers: 1 Comments: 3

∫ ((√(3x−1))/(√(2x+1))) dx

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

Question Number 85698 Answers: 0 Comments: 0

please any recommendation of a youtube video on General conics??

$$\mathrm{please}\:\mathrm{any}\:\mathrm{recommendation}\:\mathrm{of}\:\mathrm{a}\:\mathrm{youtube}\:\mathrm{video} \\ $$$$\mathrm{on}\:\mathrm{General}\:\mathrm{conics}?? \\ $$

Question Number 85696 Answers: 0 Comments: 0

Montrer que: (√5)+(√(30))+(√(50))<(√(10))+(√(20))+(√(60)) {niveau second)

$$\mathrm{Montrer}\:\mathrm{que}: \\ $$$$\sqrt{\mathrm{5}}+\sqrt{\mathrm{30}}+\sqrt{\mathrm{50}}<\sqrt{\mathrm{10}}+\sqrt{\mathrm{20}}+\sqrt{\mathrm{60}} \\ $$$$\left\{\mathrm{niveau}\:\mathrm{second}\right) \\ $$

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