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Question Number 163496 Answers: 1 Comments: 0

∫_0 ^(π/2) 256cos^5 ((x/2))sin^(11) ((x/2))dx

$$\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{256}\boldsymbol{{cos}}^{\mathrm{5}} \left(\frac{\boldsymbol{{x}}}{\mathrm{2}}\right)\boldsymbol{{sin}}^{\mathrm{11}} \left(\frac{\boldsymbol{{x}}}{\mathrm{2}}\right)\boldsymbol{{dx}} \\ $$

Question Number 163490 Answers: 1 Comments: 0

∫_0 ^∞ (x^3 /(e^x −1)) dx

$$\int_{\mathrm{0}} ^{\infty} \:\frac{\boldsymbol{{x}}^{\mathrm{3}} }{\boldsymbol{{e}}^{\boldsymbol{{x}}} \:−\mathrm{1}}\:\boldsymbol{{dx}} \\ $$

Question Number 163487 Answers: 1 Comments: 0

Ω= ∫_0 ^( 1) (( sin^( 2) ( ln(x )). ln (x))/( (√x))) dx=? −−−−−

$$ \\ $$$$\:\Omega=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{sin}^{\:\mathrm{2}} \left(\:\mathrm{ln}\left({x}\:\right)\right).\:\mathrm{ln}\:\left({x}\right)}{\:\sqrt{{x}}}\:{dx}=? \\ $$$$\:\:\:\:−−−−− \\ $$

Question Number 163484 Answers: 0 Comments: 0

pour tout couple (a,b)εR^2 ,prouver que ∫_0 ^1 t^p (lnt)^q dt converge puis calculer

$${pour}\:{tout}\:{couple}\:\left({a},{b}\right)\epsilon{R}^{\mathrm{2}} ,{prouver}\:{que} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} {t}^{{p}} \left({lnt}\right)^{{q}} {dt}\:{converge}\:{puis}\:{calculer} \\ $$

Question Number 163483 Answers: 4 Comments: 0

Question Number 163481 Answers: 1 Comments: 0

Question Number 163473 Answers: 0 Comments: 2

Question Number 163472 Answers: 1 Comments: 0

∫_0 ^3 ((xdx)/(x^3 + 2x^2 + x 2)) =

$$\int_{\mathrm{0}} ^{\mathrm{3}} \:\frac{\boldsymbol{\mathrm{xdx}}}{\boldsymbol{\mathrm{x}}^{\mathrm{3}} \:+\:\mathrm{2}\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:+\:\boldsymbol{\mathrm{x}}\:\mathrm{2}}\:= \\ $$

Question Number 163470 Answers: 0 Comments: 0

Question Number 163469 Answers: 1 Comments: 1

Question Number 163468 Answers: 0 Comments: 0

Question Number 163467 Answers: 1 Comments: 0

Question Number 163463 Answers: 1 Comments: 0

nature de la serie Σ_(n=1) ((1/(n+1))+(1/n))

$${nature}\:{de}\:{la}\:{serie} \\ $$$$\underset{{n}=\mathrm{1}} {\sum}\left(\frac{\mathrm{1}}{{n}+\mathrm{1}}+\frac{\mathrm{1}}{{n}}\right) \\ $$

Question Number 163457 Answers: 0 Comments: 1

let a>0 and 𝛌>0 fixed solve for (0;∞) the equation: 2a^2 cos((x/(2λ)) - ((2λ)/x)) = a^(x/𝛌) + a^((4𝛌)/x)

$$\mathrm{let}\:\:\boldsymbol{\mathrm{a}}>\mathrm{0}\:\:\mathrm{and}\:\:\boldsymbol{\lambda}>\mathrm{0}\:\:\mathrm{fixed} \\ $$$$\mathrm{solve}\:\mathrm{for}\:\:\left(\mathrm{0};\infty\right)\:\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\mathrm{2a}^{\mathrm{2}} \mathrm{cos}\left(\frac{\mathrm{x}}{\mathrm{2}\lambda}\:-\:\frac{\mathrm{2}\lambda}{\mathrm{x}}\right)\:=\:\mathrm{a}^{\frac{\boldsymbol{\mathrm{x}}}{\boldsymbol{\lambda}}} \:\:+\:\:\mathrm{a}^{\frac{\mathrm{4}\boldsymbol{\lambda}}{\boldsymbol{\mathrm{x}}}} \\ $$

Question Number 163452 Answers: 1 Comments: 1

Solve for real numbers: 3^(x (√x)) + 3^(1 + (1/( (√x)))) = 12

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\mathrm{3}^{\boldsymbol{\mathrm{x}}\:\sqrt{\boldsymbol{\mathrm{x}}}} \:\:+\:\:\mathrm{3}^{\mathrm{1}\:+\:\frac{\mathrm{1}}{\:\sqrt{\boldsymbol{\mathrm{x}}}}} \:\:=\:\mathrm{12} \\ $$

Question Number 163451 Answers: 0 Comments: 1

Solve for real numbers: (√(1 - x)) = 1 - 2x^2 + 2x (√(1 - x^2 ))

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\sqrt{\mathrm{1}\:-\:\mathrm{x}}\:=\:\mathrm{1}\:-\:\mathrm{2x}^{\mathrm{2}} \:+\:\mathrm{2x}\:\sqrt{\mathrm{1}\:-\:\mathrm{x}^{\mathrm{2}} } \\ $$

Question Number 163443 Answers: 0 Comments: 7

p ≤ n find (A_n ^p /A_(n−1) ^p ).

$$\mathrm{p}\:\leqslant\:\mathrm{n}\: \\ $$$$\mathrm{find}\:\:\frac{\mathrm{A}_{\mathrm{n}} ^{\mathrm{p}} }{\mathrm{A}_{\mathrm{n}−\mathrm{1}} ^{\mathrm{p}} }. \\ $$

Question Number 163441 Answers: 0 Comments: 0

∫((x+3)/((x+1)^4 ))dx=∫((x+1+3)/((x+1)^4 ))dx=∫(1/((x+1)^3 ))dx+3∫(1/((x+1)^4 ))dx

$$\int\frac{{x}+\mathrm{3}}{\left({x}+\mathrm{1}\right)^{\mathrm{4}} }{dx}=\int\frac{{x}+\mathrm{1}+\mathrm{3}}{\left({x}+\mathrm{1}\right)^{\mathrm{4}} }{dx}=\int\frac{\mathrm{1}}{\left({x}+\mathrm{1}\right)^{\mathrm{3}} }{dx}+\mathrm{3}\int\frac{\mathrm{1}}{\left({x}+\mathrm{1}\right)^{\mathrm{4}} }{dx} \\ $$

Question Number 163439 Answers: 0 Comments: 0

Question Number 163437 Answers: 1 Comments: 2

Question Number 163434 Answers: 0 Comments: 0

Question Number 163433 Answers: 0 Comments: 0

Question Number 163432 Answers: 1 Comments: 0

Question Number 163430 Answers: 1 Comments: 0

Question Number 163428 Answers: 0 Comments: 2

jusgifier la convergence de ∫_0 ^1 ln(1−x^2 )dx

$${jusgifier}\:{la}\:{convergence}\:{de}\: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}−{x}^{\mathrm{2}} \right){dx} \\ $$

Question Number 163414 Answers: 1 Comments: 0

∫(dx/( (√(cosx sin^3 x))+(√(sinx cos^3 x))))

$$\int\frac{\boldsymbol{{dx}}}{\:\sqrt{\boldsymbol{{cosx}}\:\boldsymbol{{sin}}^{\mathrm{3}} \boldsymbol{{x}}}+\sqrt{\boldsymbol{{sinx}}\:\boldsymbol{{cos}}^{\mathrm{3}} \boldsymbol{{x}}}} \\ $$

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