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AllQuestion and Answers: Page 551

Question Number 163833 Answers: 1 Comments: 12

Question Number 163829 Answers: 3 Comments: 1

∫(1/(cos x))

$$\int\frac{\mathrm{1}}{\mathrm{cos}\:{x}} \\ $$

Question Number 163828 Answers: 2 Comments: 0

∫(e^x /x)

$$\int\frac{{e}^{{x}} }{{x}} \\ $$

Question Number 163825 Answers: 2 Comments: 0

lim_(x→0) ((tan 2x−2x)/(sin 3x−3x)) =?

$$\:\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:\mathrm{2}{x}−\mathrm{2}{x}}{\mathrm{sin}\:\mathrm{3}{x}−\mathrm{3}{x}}\:=?\: \\ $$

Question Number 163834 Answers: 0 Comments: 0

∫_0 ^∞ ((t(e^(4t) −1)(ln(i)+t))/e^(2t) )dt=? by M.A

$$\int_{\mathrm{0}} ^{\infty} \frac{\boldsymbol{{t}}\left(\boldsymbol{{e}}^{\mathrm{4}\boldsymbol{{t}}} −\mathrm{1}\right)\left(\boldsymbol{{ln}}\left(\boldsymbol{{i}}\right)+\boldsymbol{{t}}\right)}{\boldsymbol{{e}}^{\mathrm{2}\boldsymbol{{t}}} }\boldsymbol{{dt}}=? \\ $$$$\boldsymbol{{by}}\:\:\boldsymbol{{M}}.\boldsymbol{{A}} \\ $$

Question Number 163822 Answers: 2 Comments: 0

sin(4x) − sin(3x) = sin(2x) find x ?

$${sin}\left(\mathrm{4}{x}\right)\:−\:{sin}\left(\mathrm{3}{x}\right)\:=\:{sin}\left(\mathrm{2}{x}\right)\:{find}\:{x}\:? \\ $$

Question Number 163812 Answers: 2 Comments: 0

Question Number 163845 Answers: 1 Comments: 0

a, b ∈ N , gcd( a , b )=1 prove that a^( ϕ (b )) + b^( ϕ (a )) ≡^( ab) 1 ϕ : Euler phi function ...

$$ \\ $$$$\:\:\:\:\:\:\:{a},\:{b}\:\in\:\mathbb{N}\:\:,\:\:{gcd}\left(\:{a}\:,\:\:{b}\:\right)=\mathrm{1} \\ $$$$\:\:\:\:\:{prove}\:\:{that}\: \\ $$$$\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{a}^{\:\:\varphi\:\left({b}\:\right)} +\:{b}^{\:\varphi\:\left({a}\:\right)} \:\overset{\:{ab}} {\equiv}\:\mathrm{1} \\ $$$$\:\:\:\:\:\varphi\::\:\:\:\mathscr{E}{uler}\:{phi}\:\:{function}\:... \\ $$$$ \\ $$

Question Number 163798 Answers: 2 Comments: 0

by a simple method calculate Σ_(k=0) ^n COS(kx)

$$ \\ $$$$\:\:\:\:{by}\:{a}\:{simple}\:{method}\:{calculate}\:\:\: \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\sum_{{k}=\mathrm{0}} ^{{n}} {COS}\left({kx}\right) \\ $$$$ \\ $$$$ \\ $$

Question Number 163789 Answers: 0 Comments: 1

∫_0 ^1 ((arccotgh(x))/(1−x^2 ))dx=? by M.A

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{{arccotgh}}\left(\boldsymbol{{x}}\right)}{\mathrm{1}−\boldsymbol{{x}}^{\mathrm{2}} }\boldsymbol{{dx}}=? \\ $$$$\boldsymbol{{by}}\:\boldsymbol{{M}}.\boldsymbol{{A}} \\ $$

Question Number 163785 Answers: 0 Comments: 0

∫_0 ^1 ((ln(x−1)ln(1−x))/x)dx=? ∫_0 ^1 ((ln(x−1)ln(1+x))/x)dx=? by M.A

Question Number 163782 Answers: 1 Comments: 1

Question Number 163786 Answers: 1 Comments: 0

Question Number 163775 Answers: 1 Comments: 1

Question Number 163763 Answers: 3 Comments: 1

$$ \\ $$

Question Number 163759 Answers: 3 Comments: 0

∫_0 ^1 (((ln(1+x))/x))^2 dx=? by M.A

$$\int_{\mathrm{0}} ^{\mathrm{1}} \left(\frac{\boldsymbol{\mathrm{ln}}\left(\mathrm{1}+\boldsymbol{\mathrm{x}}\right)}{\boldsymbol{\mathrm{x}}}\right)^{\mathrm{2}} \boldsymbol{\mathrm{dx}}=? \\ $$$$\boldsymbol{\mathrm{by}}\:\boldsymbol{\mathrm{M}}.\boldsymbol{\mathrm{A}} \\ $$

Question Number 163751 Answers: 1 Comments: 0

∫_0 ^1 ln(1+x)ln(1−x)dx=? by MATH.AMIN −−−−−−−−−−−−−−−−−−−−

$$\int_{\mathrm{0}} ^{\mathrm{1}} \boldsymbol{{ln}}\left(\mathrm{1}+\boldsymbol{{x}}\right)\boldsymbol{{ln}}\left(\mathrm{1}−\boldsymbol{{x}}\right)\boldsymbol{{dx}}=? \\ $$$$\boldsymbol{{by}}\:\boldsymbol{{MATH}}.\boldsymbol{{AMIN}} \\ $$$$−−−−−−−−−−−−−−−−−−−− \\ $$

Question Number 163747 Answers: 2 Comments: 0

a^2 (a - 3b) = b^2 (b - 3a) + 27 ab = 2 find a^3 - b^3 = ?

$$\mathrm{a}^{\mathrm{2}} \left(\mathrm{a}\:-\:\mathrm{3b}\right)\:=\:\mathrm{b}^{\mathrm{2}} \left(\mathrm{b}\:-\:\mathrm{3a}\right)\:+\:\mathrm{27} \\ $$$$\mathrm{ab}\:=\:\mathrm{2} \\ $$$$\mathrm{find}\:\:\mathrm{a}^{\mathrm{3}} \:-\:\mathrm{b}^{\mathrm{3}} \:=\:? \\ $$

Question Number 163746 Answers: 3 Comments: 0

x^2 + 5y^2 - 4xy + 6y + 9 = 0 find xy=?

$$\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{5y}^{\mathrm{2}} \:-\:\mathrm{4xy}\:+\:\mathrm{6y}\:+\:\mathrm{9}\:=\:\mathrm{0} \\ $$$$\mathrm{find}\:\:\mathrm{xy}=? \\ $$

Question Number 163743 Answers: 0 Comments: 0

Question Number 163741 Answers: 0 Comments: 4

Question Number 163736 Answers: 1 Comments: 0

Question Number 163735 Answers: 0 Comments: 1

Question Number 163733 Answers: 0 Comments: 0

prove v=(√((F∙L)/m)) ?

$${prove}\:{v}=\sqrt{\frac{{F}\centerdot{L}}{{m}}}\:\:\:? \\ $$

Question Number 163732 Answers: 0 Comments: 0

If , 𝛗 = ∫_(−∞) ^( +∞) (( sin(x).ln^( 2) (x ))/x) then find : Im (𝛗 ) = ? ■ m.n

$$ \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:\mathrm{I}{f}\:,\:\:\boldsymbol{\phi}\:=\:\int_{−\infty} ^{\:+\infty} \frac{\:{sin}\left({x}\right).{ln}^{\:\mathrm{2}} \left({x}\:\right)}{{x}}\:\:{then} \\ $$$$\:\:\:\:\:\:{find}\:\::\:\:\:\:\:\:\:\:\:\mathcal{I}{m}\:\left(\boldsymbol{\phi}\:\right)\:=\:?\:\:\:\:\:\:\:\:\:\:\blacksquare\:{m}.{n}\: \\ $$$$ \\ $$

Question Number 163730 Answers: 2 Comments: 0

Find: 𝛀 = ∫ ((sin(x) + (√3) cos(x))/(sin(3x))) dx

$$\mathrm{Find}:\:\:\boldsymbol{\Omega}\:=\:\int\:\frac{\mathrm{sin}\left(\mathrm{x}\right)\:+\:\sqrt{\mathrm{3}}\:\mathrm{cos}\left(\mathrm{x}\right)}{\mathrm{sin}\left(\mathrm{3x}\right)}\:\mathrm{dx} \\ $$

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