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Question Number 211252 Answers: 1 Comments: 0

Question Number 211251 Answers: 0 Comments: 2

Question Number 211250 Answers: 1 Comments: 0

Find the number of 4 digit numbers so that when decomposed into prime factors, have the sum of prime factors equal to the sum of the exponents?

$${Find}\:{the}\:{number}\:{of}\:\mathrm{4}\:{digit}\:{numbers} \\ $$$$\:{so}\:{that}\:{when}\:{decomposed}\:{into}\:{prime} \\ $$$$\:{factors},\:{have}\:{the}\:{sum}\:{of}\:{prime}\:{factors} \\ $$$$\:{equal}\:{to}\:{the}\:{sum}\:{of}\:{the}\:{exponents}? \\ $$

Question Number 211245 Answers: 1 Comments: 0

prove: ∫_0 ^∞ (t^(α−1) /(t^π +1))dt=(1/(sin α))

$$\mathrm{prove}: \\ $$$$\underset{\mathrm{0}} {\overset{\infty} {\int}}\frac{{t}^{\alpha−\mathrm{1}} }{{t}^{\pi} +\mathrm{1}}{dt}=\frac{\mathrm{1}}{\mathrm{sin}\:\alpha} \\ $$

Question Number 211241 Answers: 1 Comments: 4

lim_(x→0) ((cos x^2 −cos (sin^2 x ))/x^6 ) =?

$$\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\mathrm{x}^{\mathrm{2}} −\mathrm{cos}\:\left(\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}\:\right)}{\mathrm{x}^{\mathrm{6}} }\:=? \\ $$

Question Number 211235 Answers: 2 Comments: 1

Question Number 211232 Answers: 1 Comments: 0

Question Number 211231 Answers: 0 Comments: 0

Question Number 211230 Answers: 0 Comments: 0

Question Number 211277 Answers: 0 Comments: 4

Question Number 211222 Answers: 1 Comments: 0

How many integers are there such that, 0≤n≤720 and n^2 ≡1(mod)720?

$${How}\:{many}\:{integers}\:{are}\:{there} \\ $$$$\:\:\:{such}\:{that},\:\:\mathrm{0}\leqslant{n}\leqslant\mathrm{720}\:{and}\: \\ $$$$\:\:\:{n}^{\mathrm{2}} \equiv\mathrm{1}\left({mod}\right)\mathrm{720}? \\ $$

Question Number 211216 Answers: 2 Comments: 0

Question Number 211207 Answers: 2 Comments: 0

Question Number 211201 Answers: 5 Comments: 0

((x−1))^(1/3) + ((x−2))^(1/3) −((2x−3))^(1/3) = 0 x=?

$$\:\:\:\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{1}}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{2}}\:−\sqrt[{\mathrm{3}}]{\mathrm{2x}−\mathrm{3}}\:=\:\mathrm{0} \\ $$$$\:\:\:\mathrm{x}=? \\ $$

Question Number 211191 Answers: 2 Comments: 0

Question Number 211188 Answers: 1 Comments: 0

Question Number 211184 Answers: 3 Comments: 0

Question Number 211190 Answers: 3 Comments: 0

Question Number 211157 Answers: 1 Comments: 1

Question Number 211155 Answers: 1 Comments: 0

∫(((sin^n (θ)−sin (θ))^(1/n) cos (θ))/(sin^(n+1) (θ)))dθ

$$\int\frac{\left(\mathrm{sin}\:^{{n}} \left(\theta\right)−\mathrm{sin}\:\left(\theta\right)\right)^{\frac{\mathrm{1}}{{n}}} \mathrm{cos}\:\left(\theta\right)}{\mathrm{sin}\:^{{n}+\mathrm{1}} \left(\theta\right)}{d}\theta \\ $$$$ \\ $$

Question Number 211152 Answers: 1 Comments: 0

∫((√x)/(1+x+x^2 +x^3 ))dx

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\frac{\sqrt{{x}}}{\mathrm{1}+{x}+{x}^{\mathrm{2}} +{x}^{\mathrm{3}} }{dx} \\ $$$$ \\ $$

Question Number 211151 Answers: 2 Comments: 0

∫(dx/(xln x(ln ln x−1)(ln ln x−2)(ln ln x−3)(ln ln x−4)))

$$ \\ $$$$ \\ $$$$\int\frac{{dx}}{{x}\mathrm{ln}\:{x}\left(\mathrm{ln}\:\mathrm{ln}\:{x}−\mathrm{1}\right)\left(\mathrm{ln}\:\mathrm{ln}\:{x}−\mathrm{2}\right)\left(\mathrm{ln}\:\mathrm{ln}\:{x}−\mathrm{3}\right)\left(\mathrm{ln}\:\mathrm{ln}\:{x}−\mathrm{4}\right)} \\ $$$$ \\ $$$$ \\ $$

Question Number 211150 Answers: 1 Comments: 1

∫_0 ^(π/2) (tan^2 θ+tan^5 θ)e^(tan^2 θ) dθ

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \left(\mathrm{tan}\:^{\mathrm{2}} \theta+\mathrm{tan}\:^{\mathrm{5}} \theta\right){e}^{\mathrm{tan}\:^{\mathrm{2}} \theta} {d}\theta \\ $$$$ \\ $$$$ \\ $$

Question Number 211149 Answers: 0 Comments: 0

Question Number 211167 Answers: 2 Comments: 1

Question Number 211147 Answers: 1 Comments: 0

1414; 1515; 1616;...; From 5757 units How many of them are divided by 13 and the remainder is 10?

$$ \\ $$1414; 1515; 1616;...; From 5757 units How many of them are divided by 13 and the remainder is 10?

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