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Question Number 151374 Answers: 0 Comments: 0

Ω = ∫_0 ^( ∞) (( ln ((1/x) ))/(1 +e^( 2x) )) dx =^? (3/2) ln^( 2) ( 2 ) m.n

$$ \\ $$$$\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:{ln}\:\left(\frac{\mathrm{1}}{{x}}\:\right)}{\mathrm{1}\:+{e}^{\:\mathrm{2}{x}} }\:{dx}\:\overset{?} {=}\:\frac{\mathrm{3}}{\mathrm{2}}\:{ln}^{\:\mathrm{2}} \left(\:\mathrm{2}\:\right) \\ $$$$\:\:{m}.{n} \\ $$

Question Number 151371 Answers: 1 Comments: 0

a;b∈N (a+b)^2 ∙(a-b)=128 ab=?

$$\mathrm{a};\mathrm{b}\in\mathbb{N} \\ $$$$\left(\mathrm{a}+\mathrm{b}\right)^{\mathrm{2}} \centerdot\left(\mathrm{a}-\mathrm{b}\right)=\mathrm{128} \\ $$$$\mathrm{ab}=? \\ $$

Question Number 151361 Answers: 1 Comments: 0

if x+y=45 prove that: ((1 - tan(x))/(1 - tan(y))) = tan(2y)

$$\mathrm{if}\:\:\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}=\mathrm{45}\:\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\frac{\mathrm{1}\:-\:\mathrm{tan}\left(\mathrm{x}\right)}{\mathrm{1}\:-\:\mathrm{tan}\left(\mathrm{y}\right)}\:=\:\mathrm{tan}\left(\mathrm{2y}\right) \\ $$

Question Number 151360 Answers: 0 Comments: 0

find max(ℜ(I)+ℑ(I)) for the integral I = ∫_z ^( z+1) cos(cos(cos(x^(cos(cos(cos(x)))) )))dx z ∈ R

$$\: \\ $$$$\:\:\mathrm{find}\:\mathrm{max}\left(\Re\left(\mathrm{I}\right)+\Im\left(\mathrm{I}\right)\right)\:\mathrm{for}\:\mathrm{the}\:\mathrm{integral} \\ $$$$\:\:\mathrm{I}\:=\:\int_{{z}} ^{\:{z}+\mathrm{1}} \:\mathrm{cos}\left(\mathrm{cos}\left(\mathrm{cos}\left({x}^{\mathrm{cos}\left(\mathrm{cos}\left(\mathrm{cos}\left({x}\right)\right)\right)} \right)\right)\right){dx} \\ $$$$\:\:{z}\:\in\:\mathbb{R} \\ $$$$\: \\ $$

Question Number 151357 Answers: 1 Comments: 6

Question Number 151351 Answers: 1 Comments: 0

Question Number 151350 Answers: 0 Comments: 4

Question Number 151346 Answers: 1 Comments: 0

x^2 + 5x + 25 = 0 ⇒ x^3 - 100 = ?

$$\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{5x}\:+\:\mathrm{25}\:=\:\mathrm{0}\:\:\Rightarrow\:\:\mathrm{x}^{\mathrm{3}} \:-\:\mathrm{100}\:=\:? \\ $$

Question Number 151345 Answers: 1 Comments: 0

∫_0 ^π (e^(cos x) /(e^(cos x) +e^(−cos x) ))dx

$$\int_{\mathrm{0}} ^{\pi} \frac{\mathrm{e}^{\mathrm{cos}\:\mathrm{x}} }{\mathrm{e}^{\mathrm{cos}\:\mathrm{x}} +\mathrm{e}^{−\mathrm{cos}\:\mathrm{x}} }\mathrm{dx} \\ $$

Question Number 151344 Answers: 2 Comments: 0

x^2 - 4x + 1 = 0 ⇒ x^3 + (1/x^3 ) = ?

$$\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{4x}\:+\:\mathrm{1}\:=\:\mathrm{0}\:\:\Rightarrow\:\:\mathrm{x}^{\mathrm{3}} \:+\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} }\:=\:? \\ $$

Question Number 151341 Answers: 1 Comments: 0

∫_α ^β (dx/(x(√((x−α)(β−x) ))))=(π/( (√(αβ)))) where α,β >0

$$\int_{\alpha} ^{\beta} \frac{\mathrm{dx}}{\mathrm{x}\sqrt{\left(\mathrm{x}−\alpha\right)\left(\beta−\mathrm{x}\right)\:}}=\frac{\pi}{\:\sqrt{\alpha\beta}} \\ $$$$\mathrm{where}\:\alpha,\beta\:>\mathrm{0} \\ $$

Question Number 151340 Answers: 1 Comments: 0

Evaluate ∫_(−1) ^1 (((2x^(332) +x^(998) +4x^(1668) .sin x^(691) ))/(1+x^(666) ))dx

$$\mathrm{Evaluate} \\ $$$$\int_{−\mathrm{1}} ^{\mathrm{1}} \frac{\left(\mathrm{2x}^{\mathrm{332}} +\mathrm{x}^{\mathrm{998}} +\mathrm{4x}^{\mathrm{1668}} .\mathrm{sin}\:\mathrm{x}^{\mathrm{691}} \right)}{\mathrm{1}+\mathrm{x}^{\mathrm{666}} }\mathrm{dx} \\ $$

Question Number 151332 Answers: 1 Comments: 2

which is larger? 2^(√(10)) or 3^2

$$\mathrm{which}\:\mathrm{is}\:\mathrm{larger}? \\ $$$$\mathrm{2}^{\sqrt{\mathrm{10}}} \:\:\mathrm{or}\:\:\mathrm{3}^{\mathrm{2}} \\ $$

Question Number 151322 Answers: 1 Comments: 1

Determine all pairs (x;y) of integers which satisfy: x^3 - 3x + y = 0

$$\mathrm{Determine}\:\mathrm{all}\:\mathrm{pairs}\:\:\left(\mathrm{x};\mathrm{y}\right)\:\:\mathrm{of}\:\mathrm{integers} \\ $$$$\mathrm{which}\:\mathrm{satisfy}: \\ $$$$\mathrm{x}^{\mathrm{3}} \:-\:\mathrm{3x}\:+\:\mathrm{y}\:=\:\mathrm{0} \\ $$

Question Number 151321 Answers: 0 Comments: 0

Question Number 151317 Answers: 2 Comments: 0

if x=(((√7) - (√6)))^(1/3) + (((√7) + (√6)))^(1/3) find E(x) = x^6 - 6x^4 + 9x^2 = ?

$$\mathrm{if}\:\:\boldsymbol{\mathrm{x}}=\sqrt[{\mathrm{3}}]{\sqrt{\mathrm{7}}\:-\:\sqrt{\mathrm{6}}}\:+\:\sqrt[{\mathrm{3}}]{\sqrt{\mathrm{7}}\:+\:\sqrt{\mathrm{6}}} \\ $$$$\mathrm{find}\:\:\mathrm{E}\left(\mathrm{x}\right)\:=\:\mathrm{x}^{\mathrm{6}} \:-\:\mathrm{6x}^{\mathrm{4}} \:+\:\mathrm{9x}^{\mathrm{2}} \:=\:? \\ $$

Question Number 151316 Answers: 1 Comments: 0

Find positive integers a and b such that ((a)^(1/3) +(b)^(1/3) −1)^2 = 49+ 20(6)^(1/3)

$$\:\:\:\:\:\:{Find}\:{positive}\:{integers}\: \\ $$$$\:\:\:\:\:{a}\:{and}\:{b}\:{such}\:{that}\: \\ $$$$\:\:\:\:\:\left(\sqrt[{\mathrm{3}}]{{a}}\:+\sqrt[{\mathrm{3}}]{{b}}\:−\mathrm{1}\right)^{\mathrm{2}} =\:\mathrm{49}+\:\mathrm{20}\sqrt[{\mathrm{3}}]{\mathrm{6}}\: \\ $$

Question Number 151315 Answers: 1 Comments: 0

if x^2 +y^2 =16^2 ; y^2 +z^2 =24^2 z^2 +t^2 =42^2 and t^2 +x^2 =38^2 find max[(x+z)(y+t)]=?

$$\mathrm{if}\:\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} =\mathrm{16}^{\mathrm{2}} \:\:;\:\:\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} =\mathrm{24}^{\mathrm{2}} \\ $$$$\mathrm{z}^{\mathrm{2}} +\mathrm{t}^{\mathrm{2}} =\mathrm{42}^{\mathrm{2}} \:\:\mathrm{and}\:\:\mathrm{t}^{\mathrm{2}} +\mathrm{x}^{\mathrm{2}} =\mathrm{38}^{\mathrm{2}} \\ $$$$\mathrm{find}\:\:\mathrm{max}\left[\left(\mathrm{x}+\mathrm{z}\right)\left(\mathrm{y}+\mathrm{t}\right)\right]=? \\ $$

Question Number 151311 Answers: 0 Comments: 0

Question Number 151308 Answers: 0 Comments: 0

Question Number 151307 Answers: 2 Comments: 0

if x(√x) - 26(√x) = 5 find x - 5(√x) = ?

$$\mathrm{if}\:\:\mathrm{x}\sqrt{\mathrm{x}}\:-\:\mathrm{26}\sqrt{\mathrm{x}}\:=\:\mathrm{5} \\ $$$$\mathrm{find}\:\:\mathrm{x}\:-\:\mathrm{5}\sqrt{\mathrm{x}}\:=\:? \\ $$

Question Number 151300 Answers: 3 Comments: 0

5 ∙ 6,02∙10^(23) = ? (solution) a)3,01∙10^(24) b)3,01∙10^(22)

$$\mathrm{5}\:\centerdot\:\mathrm{6},\mathrm{02}\centerdot\mathrm{10}^{\mathrm{23}} \:=\:?\:\left(\mathrm{solution}\right) \\ $$$$\left.\mathrm{a}\left.\right)\mathrm{3},\mathrm{01}\centerdot\mathrm{10}^{\mathrm{24}} \:\:\:\mathrm{b}\right)\mathrm{3},\mathrm{01}\centerdot\mathrm{10}^{\mathrm{22}} \\ $$

Question Number 151294 Answers: 1 Comments: 0

Question Number 151287 Answers: 0 Comments: 2

I = ∫_(x=a) ^( x=b) (√(u^2 + v^2 x^2 − 2uvwx)) dx = ?

$${I}\:=\:\int_{{x}={a}} ^{\:{x}={b}} \sqrt{{u}^{\mathrm{2}} \:+\:{v}^{\mathrm{2}} {x}^{\mathrm{2}} \:−\:\mathrm{2}{uvwx}}\:{dx}\:=\:? \\ $$

Question Number 151284 Answers: 1 Comments: 0

if (a/3^(x-1) ) = (b/3^(y+2) ) = (c/3^(z-1) ) = (1/5) find abc = ?

$$\mathrm{if}\:\:\frac{\mathrm{a}}{\mathrm{3}^{\boldsymbol{\mathrm{x}}-\mathrm{1}} }\:=\:\frac{\mathrm{b}}{\mathrm{3}^{\boldsymbol{\mathrm{y}}+\mathrm{2}} }\:=\:\frac{\mathrm{c}}{\mathrm{3}^{\boldsymbol{\mathrm{z}}-\mathrm{1}} }\:=\:\frac{\mathrm{1}}{\mathrm{5}} \\ $$$$\mathrm{find}\:\:\mathrm{abc}\:=\:? \\ $$

Question Number 151282 Answers: 0 Comments: 0

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