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Question Number 154352 Answers: 0 Comments: 0

∫(x^(n−1) /(x^(3n+1) (x^n −1)))dx=?

$$\:\int\frac{{x}^{{n}−\mathrm{1}} }{{x}^{\mathrm{3}{n}+\mathrm{1}} \left({x}^{{n}} −\mathrm{1}\right)}{dx}=? \\ $$

Question Number 154351 Answers: 3 Comments: 0

∫_(−1) ^( 0) ((x−1)/( (√(x^2 −4x+3)) )) dx =?

$$\int_{−\mathrm{1}} ^{\:\mathrm{0}} \:\frac{{x}−\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{3}}\:}\:{dx}\:=? \\ $$

Question Number 154343 Answers: 1 Comments: 0

Question Number 154337 Answers: 2 Comments: 0

etudier la continuite, et derivabilite: x^2 sin((1/x)) si≠0 et f(0)=0

$${etudier}\:{la}\:{continuite},\:{et}\:{derivabilite}: \\ $$$${x}^{\mathrm{2}} {sin}\left(\frac{\mathrm{1}}{{x}}\right)\:{si}\neq\mathrm{0}\:{et}\:{f}\left(\mathrm{0}\right)=\mathrm{0} \\ $$

Question Number 154334 Answers: 3 Comments: 1

the n^(th) term of 1 , 2, 6, 24, 120 ........ is?

$${the}\:{n}^{{th}} \:{term}\:{of} \\ $$$$\mathrm{1}\:,\:\mathrm{2},\:\mathrm{6},\:\mathrm{24},\:\mathrm{120}\:........\:{is}? \\ $$

Question Number 154328 Answers: 2 Comments: 0

S=(1/(1+10))+(2/(1+10^2 ))+(4/(1+10^4 ))+(8/(1+10^8 ))+…

$$\:{S}=\frac{\mathrm{1}}{\mathrm{1}+\mathrm{10}}+\frac{\mathrm{2}}{\mathrm{1}+\mathrm{10}^{\mathrm{2}} }+\frac{\mathrm{4}}{\mathrm{1}+\mathrm{10}^{\mathrm{4}} }+\frac{\mathrm{8}}{\mathrm{1}+\mathrm{10}^{\mathrm{8}} }+\ldots\: \\ $$$$ \\ $$

Question Number 154330 Answers: 1 Comments: 0

Question Number 154321 Answers: 2 Comments: 0

Question Number 154316 Answers: 1 Comments: 0

If x^3 + (1/y^3 ) = y^3 + (1/z^3 ) = 1 Find (xyz)^(2025) - 1 = ?

$$\mathrm{If}\:\:\mathrm{x}^{\mathrm{3}} \:+\:\frac{\mathrm{1}}{\mathrm{y}^{\mathrm{3}} }\:=\:\mathrm{y}^{\mathrm{3}} \:+\:\frac{\mathrm{1}}{\mathrm{z}^{\mathrm{3}} }\:=\:\mathrm{1} \\ $$$$\mathrm{Find}\:\:\left(\mathrm{xyz}\right)^{\mathrm{2025}} \:-\:\mathrm{1}\:=\:? \\ $$

Question Number 154320 Answers: 1 Comments: 0

if a;b;c>0 and ab+bc+ca=2 then: Σ_(cyc) ((a(b^4 + c^4 ))/(b^3 + b^2 c + bc^2 + c^3 )) ≥ 1

$$\mathrm{if}\:\:\mathrm{a};\mathrm{b};\mathrm{c}>\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{ab}+\mathrm{bc}+\mathrm{ca}=\mathrm{2}\:\:\mathrm{then}: \\ $$$$\underset{\boldsymbol{\mathrm{cyc}}} {\sum}\:\frac{\mathrm{a}\left(\mathrm{b}^{\mathrm{4}} \:+\:\mathrm{c}^{\mathrm{4}} \right)}{\mathrm{b}^{\mathrm{3}} \:+\:\mathrm{b}^{\mathrm{2}} \mathrm{c}\:+\:\mathrm{bc}^{\mathrm{2}} \:+\:\mathrm{c}^{\mathrm{3}} }\:\geqslant\:\mathrm{1} \\ $$

Question Number 154318 Answers: 1 Comments: 0

Question Number 154309 Answers: 1 Comments: 0

Question Number 154306 Answers: 0 Comments: 1

Question Number 154303 Answers: 1 Comments: 1

Solve in R ((z^9 - 81z - 62)/z^3 ) = 18 ((3z + 2))^(1/3)

$$\mathrm{Solve}\:\mathrm{in}\:\mathbb{R} \\ $$$$\frac{\mathrm{z}^{\mathrm{9}} \:-\:\mathrm{81z}\:-\:\mathrm{62}}{\mathrm{z}^{\mathrm{3}} }\:=\:\mathrm{18}\:\sqrt[{\mathrm{3}}]{\mathrm{3z}\:+\:\mathrm{2}} \\ $$

Question Number 154301 Answers: 1 Comments: 0

of the integers 101 to 400 (including 101 and 400 themselves) how many are not divisible by 3 or 5?

$$\mathrm{of}\:\mathrm{the}\:\mathrm{integers}\:\mathrm{101}\:\mathrm{to}\:\mathrm{400}\:\left(\mathrm{including}\:\mathrm{101}\:\mathrm{and}\:\mathrm{400}\:\right. \\ $$$$\left.\mathrm{themselves}\right)\:\mathrm{how}\:\mathrm{many}\:\mathrm{are}\:\mathrm{not}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{3}\:\mathrm{or}\:\mathrm{5}? \\ $$

Question Number 154296 Answers: 0 Comments: 0

Question Number 154292 Answers: 2 Comments: 0

Question Number 154291 Answers: 2 Comments: 0

Among the integers 101−400,how many numbers are divisible by 3 but no divisible by 5 or 7

$$\mathrm{Among}\:\mathrm{the}\:\mathrm{integers}\:\mathrm{101}−\mathrm{400},\mathrm{how}\:\mathrm{many}\:\mathrm{numbers} \\ $$$$\mathrm{are}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{3}\:\mathrm{but}\:\mathrm{no}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{5}\:\mathrm{or}\:\mathrm{7} \\ $$

Question Number 154289 Answers: 0 Comments: 0

solve ∫4x^(5x) dx=?

$${solve}\: \\ $$$$\int\mathrm{4}{x}^{\mathrm{5}{x}} {dx}=? \\ $$

Question Number 154287 Answers: 0 Comments: 0

Question Number 154285 Answers: 0 Comments: 0

Question Number 154286 Answers: 1 Comments: 5

h = ((52−47i))^(1/3) +((52+47i))^(1/3) find h^2 .

$$\:{h}\:=\:\sqrt[{\mathrm{3}}]{\mathrm{52}−\mathrm{47}{i}}\:+\sqrt[{\mathrm{3}}]{\mathrm{52}+\mathrm{47}{i}}\: \\ $$$$\:{find}\:{h}^{\mathrm{2}} . \\ $$

Question Number 154281 Answers: 0 Comments: 0

∫_1 ^3 ⌊x−3⌋dx

$$\int_{\mathrm{1}} ^{\mathrm{3}} \lfloor{x}−\mathrm{3}\rfloor{dx} \\ $$

Question Number 154280 Answers: 0 Comments: 0

∫_0 ^( 1) ∫_0 ^( z^2 ) ∫_0 ^( 3) y cos (z^5 )dxdydz =?

$$\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:{z}^{\mathrm{2}} } \int_{\mathrm{0}} ^{\:\mathrm{3}} {y}\:\mathrm{cos}\:\left({z}^{\mathrm{5}} \right){dxdydz}\:=? \\ $$

Question Number 154275 Answers: 0 Comments: 1

Question Number 154274 Answers: 0 Comments: 1

Solve the equation: x^2 ∙2^x (x^4 ∙4^x + 3∙15^x ) = 125^x - 27^x

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\mathrm{x}^{\mathrm{2}} \centerdot\mathrm{2}^{\boldsymbol{\mathrm{x}}} \left(\mathrm{x}^{\mathrm{4}} \centerdot\mathrm{4}^{\boldsymbol{\mathrm{x}}} \:+\:\mathrm{3}\centerdot\mathrm{15}^{\boldsymbol{\mathrm{x}}} \right)\:=\:\mathrm{125}^{\boldsymbol{\mathrm{x}}} \:-\:\mathrm{27}^{\boldsymbol{\mathrm{x}}} \\ $$

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