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Question Number 64676 Answers: 0 Comments: 0

z^4 −12iz−100=0

$${z}^{\mathrm{4}} −\mathrm{12}{iz}−\mathrm{100}=\mathrm{0} \\ $$

Question Number 64662 Answers: 1 Comments: 3

∫(dx/((x^8 +x^4 +1)^2 )) ∫_(1/x) ^x ((ln(t))/(t^2 +1)) dt

$$\int\frac{{dx}}{\left({x}^{\mathrm{8}} +{x}^{\mathrm{4}} +\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$ \\ $$$$\int_{\frac{\mathrm{1}}{{x}}} ^{{x}} \frac{{ln}\left({t}\right)}{{t}^{\mathrm{2}} +\mathrm{1}}\:{dt} \\ $$

Question Number 64652 Answers: 0 Comments: 2

calculate S_n =Σ_(k=0) ^n k (C_n ^k )^2

$${calculate}\:\:{S}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:{k}\:\left({C}_{{n}} ^{{k}} \right)^{\mathrm{2}} \\ $$

Question Number 64651 Answers: 1 Comments: 1

calculate Σ_(k=1) ^n kC_n ^k 3^k interms of n

$${calculate}\:\sum_{{k}=\mathrm{1}} ^{{n}} {kC}_{{n}} ^{{k}} \:\mathrm{3}^{{k}} \:\:{interms}\:{of}\:{n} \\ $$

Question Number 64650 Answers: 0 Comments: 1

U_n is a sequence wich verify lim_(n→+∞) U_(n+1) −U_n =a calculate lim_(n→+∞) (U_n /n)

$${U}_{{n}} \:{is}\:{a}\:{sequence}\:{wich}\:{verify}\:{lim}_{{n}\rightarrow+\infty} {U}_{{n}+\mathrm{1}} −{U}_{{n}} ={a}\:\:\: \\ $$$${calculate}\:{lim}_{{n}\rightarrow+\infty} \:\frac{{U}_{{n}} }{{n}} \\ $$

Question Number 64649 Answers: 1 Comments: 1

calculate ∫_0 ^(2π) ((cosθ)/(5+3cosθ))dθ

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{cos}\theta}{\mathrm{5}+\mathrm{3}{cos}\theta}{d}\theta \\ $$

Question Number 64642 Answers: 0 Comments: 1

∫(dx)/e^x +x

$$\int\left({dx}\right)/{e}^{{x}} +{x} \\ $$

Question Number 64640 Answers: 1 Comments: 3

I = Σ_(n = 0) ^∞ (((− 1)^n )/(6n + 1))

$$\mathrm{I}\:\:=\:\:\underset{\mathrm{n}\:=\:\mathrm{0}} {\overset{\infty} {\sum}}\:\:\frac{\left(−\:\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{6n}\:+\:\mathrm{1}} \\ $$

Question Number 64635 Answers: 0 Comments: 1

1)calculate f(a) =∫_0 ^∞ ((arctan(αx))/(1+x^2 ))dx with α real 2) find the value of ∫_0 ^∞ ((arctan(2x))/(1+x^2 ))dx

$$\left.\mathrm{1}\right){calculate}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\frac{{arctan}\left(\alpha{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}\:\:{with}\:\alpha\:{real} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left(\mathrm{2}{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 64631 Answers: 1 Comments: 3

(√((1+2x(√(1−x^2 )))/2))+2x^2 =1 To solve in R

$$\sqrt{\frac{\mathrm{1}+\mathrm{2}{x}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{\mathrm{2}}}+\mathrm{2}{x}^{\mathrm{2}} =\mathrm{1} \\ $$$$\mathrm{To}\:\mathrm{solve}\:\mathrm{in}\:\mathbb{R} \\ $$

Question Number 64625 Answers: 2 Comments: 3

Question Number 64619 Answers: 0 Comments: 2

show that ∫_(−α) ^α sinc(x)dx=∫_(−α) ^α sinc^2 (x)dx=Π

$${show}\:{that}\:\int_{−\alpha} ^{\alpha} {sinc}\left({x}\right){dx}=\int_{−\alpha} ^{\alpha} {sinc}^{\mathrm{2}} \left({x}\right){dx}=\Pi \\ $$

Question Number 64612 Answers: 0 Comments: 3

Question Number 64610 Answers: 0 Comments: 2

Question Number 64591 Answers: 0 Comments: 0

Question Number 64604 Answers: 0 Comments: 0

find all integr naturals n and k wich verify k!=(2^n −1)(2^n −2)(2^n −4)...(2^n −2^(n−1) )

$${find}\:\:{all}\:{integr}\:{naturals}\:{n}\:{and}\:{k}\:{wich}\:{verify} \\ $$$${k}!=\left(\mathrm{2}^{{n}} −\mathrm{1}\right)\left(\mathrm{2}^{{n}} −\mathrm{2}\right)\left(\mathrm{2}^{{n}} −\mathrm{4}\right)...\left(\mathrm{2}^{{n}} −\mathrm{2}^{{n}−\mathrm{1}} \right) \\ $$

Question Number 64601 Answers: 1 Comments: 0

10^x =x^(1000) ⇒ x =?

$$\:\:\:\:\:\mathrm{10}^{{x}} ={x}^{\mathrm{1000}} \:\Rightarrow\:{x}\:=? \\ $$

Question Number 64671 Answers: 0 Comments: 1

Question Number 64580 Answers: 3 Comments: 0

a^2 +b^2 =a+b ,a^2 −b^2 =ab a=? b=? and what if a^2 +b^2 =a−b?

$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} ={a}+{b}\:,{a}^{\mathrm{2}} −{b}^{\mathrm{2}} ={ab} \\ $$$${a}=?\:{b}=? \\ $$$${and}\:{what}\:{if}\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} ={a}−{b}? \\ $$

Question Number 64579 Answers: 0 Comments: 1

∫ e^x^2 dx can we get a close form of this integral or analytic solution

$$\int\:\mathrm{e}^{\mathrm{x}^{\mathrm{2}} } \:\mathrm{dx} \\ $$$$ \\ $$$$\mathrm{can}\:\mathrm{we}\:\mathrm{get}\:\mathrm{a}\:\mathrm{close}\:\mathrm{form}\:\mathrm{of}\:\mathrm{this}\:\mathrm{integral}\:\mathrm{or}\:\mathrm{analytic}\:\mathrm{solution} \\ $$

Question Number 64574 Answers: 0 Comments: 7

Question Number 64564 Answers: 0 Comments: 2

Question Number 64561 Answers: 1 Comments: 1

Question Number 64559 Answers: 0 Comments: 1

Question Number 64557 Answers: 1 Comments: 3

Question Number 64544 Answers: 1 Comments: 1

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