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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)

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

Question Number 85695    Answers: 0   Comments: 0

Question Number 85694    Answers: 0   Comments: 1

log_(((x/(x−3)))) (7) < log_(((x/3))) (7)

$$\mathrm{log}_{\left(\frac{{x}}{{x}−\mathrm{3}}\right)} \left(\mathrm{7}\right)\:<\:\mathrm{log}_{\left(\frac{{x}}{\mathrm{3}}\right)} \:\left(\mathrm{7}\right)\: \\ $$

Question Number 85677    Answers: 2   Comments: 3

∫_0 ^π ((sin (((21x)/2)))/(sin ((x/2)))) dx

$$\underset{\mathrm{0}} {\overset{\pi} {\int}}\:\frac{\mathrm{sin}\:\left(\frac{\mathrm{21}{x}}{\mathrm{2}}\right)}{\mathrm{sin}\:\left(\frac{{x}}{\mathrm{2}}\right)}\:{dx}\: \\ $$

Question Number 85676    Answers: 0   Comments: 15

∫ _0 ^∞ (dx/((x+(√(1+x^2 )))^2 )) let x = tan t ⇒dx=sec^2 t dt ∫_0 ^(π/2) ((sec^2 t dt)/((tan t+sec t)^2 )) = ∫_0 ^(π/2) (dt/((sin t+1)^2 )) = ∫_0 ^(π/2) (dt/((cos (1/2)t+sin (1/2)t)^4 )) = ∫_0 ^(π/2) (dt/(4cos^4 ((1/2)t−(π/4)))) = (1/4)∫_0 ^(π/2) sec^4 ((1/2)t−(π/4)) dt [ let (1/2)t−(π/4)= u] = (1/4)∫_(−(π/4)) ^0 sec^4 u ×2du =(1/2)∫ _(−(π/4)) ^0 (tan^2 u+1) d(tan u) = (1/2) [(1/3)tan^3 u + tan u ]_(−(π/4)) ^0 = (1/2) [ 0−(−(1/3)−1)]= (2/3)

$$\int\underset{\mathrm{0}} {\overset{\infty} {\:}}\:\frac{{dx}}{\left({x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right)^{\mathrm{2}} } \\ $$$${let}\:{x}\:=\:\mathrm{tan}\:{t}\:\Rightarrow{dx}=\mathrm{sec}\:^{\mathrm{2}} {t}\:{dt} \\ $$$$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{\mathrm{sec}\:^{\mathrm{2}} {t}\:{dt}}{\left(\mathrm{tan}\:{t}+\mathrm{sec}\:{t}\right)^{\mathrm{2}} }\:=\: \\ $$$$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{{dt}}{\left(\mathrm{sin}\:{t}+\mathrm{1}\right)^{\mathrm{2}} }\:=\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{{dt}}{\left(\mathrm{cos}\:\frac{\mathrm{1}}{\mathrm{2}}{t}+\mathrm{sin}\:\frac{\mathrm{1}}{\mathrm{2}}{t}\right)^{\mathrm{4}} } \\ $$$$=\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{{dt}}{\mathrm{4cos}^{\mathrm{4}} \:\left(\frac{\mathrm{1}}{\mathrm{2}}{t}−\frac{\pi}{\mathrm{4}}\right)} \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{4}}\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\mathrm{sec}\:^{\mathrm{4}} \left(\frac{\mathrm{1}}{\mathrm{2}}{t}−\frac{\pi}{\mathrm{4}}\right)\:{dt} \\ $$$$\left[\:{let}\:\frac{\mathrm{1}}{\mathrm{2}}{t}−\frac{\pi}{\mathrm{4}}=\:{u}\right] \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{4}}\underset{−\frac{\pi}{\mathrm{4}}} {\overset{\mathrm{0}} {\int}}\:\mathrm{sec}\:^{\mathrm{4}} {u}\:×\mathrm{2}{du} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int\underset{−\frac{\pi}{\mathrm{4}}} {\overset{\mathrm{0}} {\:}}\left(\mathrm{tan}\:^{\mathrm{2}} {u}+\mathrm{1}\right)\:{d}\left(\mathrm{tan}\:{u}\right) \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{2}}\:\left[\frac{\mathrm{1}}{\mathrm{3}}\mathrm{tan}\:^{\mathrm{3}} {u}\:+\:\mathrm{tan}\:{u}\:\right]_{−\frac{\pi}{\mathrm{4}}} ^{\mathrm{0}} \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{2}}\:\left[\:\mathrm{0}−\left(−\frac{\mathrm{1}}{\mathrm{3}}−\mathrm{1}\right)\right]=\:\frac{\mathrm{2}}{\mathrm{3}} \\ $$$$ \\ $$

Question Number 85670    Answers: 0   Comments: 3

Question Number 85669    Answers: 1   Comments: 4

∫ ((√(1+x))/(√(1−x))) dx

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

Question Number 85668    Answers: 0   Comments: 2

z = 2 + i find arg(z)

$$\mathrm{z}\:=\:\mathrm{2}\:+\:\mathrm{i}\: \\ $$$$\mathrm{find}\:\mathrm{arg}\left(\mathrm{z}\right) \\ $$

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