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Question Number 150990 Answers: 1 Comments: 0

I = ∫_(0 ) ^( ∞) (dx/(1+x^n )) = ?

$$\: \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{I}\:=\:\int_{\mathrm{0}\:} ^{\:\infty} \:\frac{{dx}}{\mathrm{1}+{x}^{{n}} }\:=\:? \\ $$$$\: \\ $$$$\: \\ $$

Question Number 150986 Answers: 1 Comments: 0

∫_0 ^( 1) ((ln (x+1))/(x^2 +1)) dx = ?

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

Question Number 150984 Answers: 0 Comments: 0

Question Number 151073 Answers: 2 Comments: 0

the value of (((50)),(0) )^2 + (((50)),(1) )^2 + (((50)),(2) )^2 +...+ (((50)),((49)) )^2 + (((50)),((50)) )^2

$$\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\begin{pmatrix}{\mathrm{50}}\\{\mathrm{0}}\end{pmatrix}^{\mathrm{2}} +\begin{pmatrix}{\mathrm{50}}\\{\mathrm{1}}\end{pmatrix}^{\mathrm{2}} +\begin{pmatrix}{\mathrm{50}}\\{\mathrm{2}}\end{pmatrix}^{\mathrm{2}} +...+\begin{pmatrix}{\mathrm{50}}\\{\mathrm{49}}\end{pmatrix}^{\mathrm{2}} +\begin{pmatrix}{\mathrm{50}}\\{\mathrm{50}}\end{pmatrix}^{\mathrm{2}} \\ $$

Question Number 151145 Answers: 1 Comments: 0

Question Number 151144 Answers: 1 Comments: 0

Question Number 150979 Answers: 1 Comments: 0

if x=(4)^(1/3) +(2)^(1/3) +1 find (3/x)+(3/x^2 )+(1/x^3 )=?

$$\mathrm{if}\:\:\mathrm{x}=\sqrt[{\mathrm{3}}]{\mathrm{4}}+\sqrt[{\mathrm{3}}]{\mathrm{2}}+\mathrm{1}\:\:\mathrm{find}\:\:\frac{\mathrm{3}}{\mathrm{x}}+\frac{\mathrm{3}}{\mathrm{x}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} }=? \\ $$$$ \\ $$

Question Number 150977 Answers: 1 Comments: 0

Question Number 150976 Answers: 0 Comments: 0

Question Number 150974 Answers: 0 Comments: 0

Question Number 150968 Answers: 1 Comments: 0

Question Number 150967 Answers: 1 Comments: 0

E(x+(2/x))=((x^3 +1)/x) +((x^3 +8)/(2x^2 )) +3 , E(2)=?

$${E}\left({x}+\frac{\mathrm{2}}{{x}}\right)=\frac{{x}^{\mathrm{3}} +\mathrm{1}}{{x}}\:+\frac{{x}^{\mathrm{3}} +\mathrm{8}}{\mathrm{2}{x}^{\mathrm{2}} }\:+\mathrm{3}\:, \\ $$$$\:{E}\left(\mathrm{2}\right)=? \\ $$

Question Number 150966 Answers: 0 Comments: 2

if a;b∈N^+ then determine all the prime numbers p which satisfy (p + 2)^a = (p - 2)^b

$$\mathrm{if}\:\:\mathrm{a};\mathrm{b}\in\mathbb{N}^{+} \:\:\mathrm{then}\:\mathrm{determine}\:\mathrm{all}\:\mathrm{the} \\ $$$$\mathrm{prime}\:\mathrm{numbers}\:\boldsymbol{\mathrm{p}}\:\mathrm{which}\:\mathrm{satisfy} \\ $$$$\left(\mathrm{p}\:+\:\mathrm{2}\right)^{\boldsymbol{\mathrm{a}}} \:=\:\left(\mathrm{p}\:-\:\mathrm{2}\right)^{\boldsymbol{\mathrm{b}}} \\ $$

Question Number 150965 Answers: 1 Comments: 0

Question Number 150963 Answers: 1 Comments: 0

Given x ,y real number such that 0<(y/x)<(1/2). Find minimum value of ((2y)/(x−y)) +((3x)/(x+2y)) .

$${Given}\:{x}\:,{y}\:{real}\:{number}\:{such}\:{that} \\ $$$$\:\mathrm{0}<\frac{{y}}{{x}}<\frac{\mathrm{1}}{\mathrm{2}}.\:{Find}\:{minimum}\:{value} \\ $$$${of}\:\frac{\mathrm{2}{y}}{{x}−{y}}\:+\frac{\mathrm{3}{x}}{{x}+\mathrm{2}{y}}\:.\: \\ $$

Question Number 150960 Answers: 1 Comments: 1

given x ,y is a prime number with x<y and x^3 +y^3 +20l8 =30y^2 −300y+30l8 find the value of x

$$\mathrm{given}\:\mathrm{x}\:,\mathrm{y}\:\mathrm{is}\:\mathrm{a}\:\mathrm{prime}\:\mathrm{number}\: \\ $$$$\mathrm{with}\:\mathrm{x}<\mathrm{y}\:\mathrm{and}\:\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} +\mathrm{20l8}\:=\mathrm{30y}^{\mathrm{2}} −\mathrm{300y}+\mathrm{30l8} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x} \\ $$

Question Number 150941 Answers: 2 Comments: 2

∫_1 ^4 ∣x−2∣dx please help me out

$$\int_{\mathrm{1}} ^{\mathrm{4}} \mid{x}−\mathrm{2}\mid{dx} \\ $$$${please}\:{help}\:{me}\:{out} \\ $$

Question Number 150932 Answers: 1 Comments: 0

I=∫((cosx − 2sinx)/(e^(2x) −sinx))dx=^?

$$\mathrm{I}=\int\frac{\mathrm{cosx}\:−\:\mathrm{2sinx}}{\mathrm{e}^{\mathrm{2x}} −\mathrm{sinx}}\mathrm{dx}\overset{?} {=} \\ $$

Question Number 150918 Answers: 2 Comments: 2

Question Number 150916 Answers: 1 Comments: 0

x^((x−1)^2 ) =2x+1 how can it solve this ?help me please

$${x}^{\left({x}−\mathrm{1}\right)^{\mathrm{2}} } =\mathrm{2}{x}+\mathrm{1}\: \\ $$$$ \\ $$$${how}\:{can}\:{it}\:{solve}\:{this}\:?{help}\:{me}\:{please} \\ $$

Question Number 150903 Answers: 1 Comments: 0

let x,y>0 , n∈N, show that (x+y)^n ≤2^(n−1) (x^n +y^n )..

$${let}\:{x},{y}>\mathrm{0}\:,\:{n}\in\mathbb{N}, \\ $$$${show}\:{that}\:\left({x}+{y}\right)^{{n}} \leqslant\mathrm{2}^{{n}−\mathrm{1}} \left({x}^{{n}} +{y}^{{n}} \right).. \\ $$

Question Number 150895 Answers: 1 Comments: 1

Question Number 150889 Answers: 1 Comments: 0

Question Number 150887 Answers: 1 Comments: 4

Question Number 150886 Answers: 0 Comments: 0

ϕ(n)=ϕ(n+1)=ϕ(n+2) n∈N n_(min) =? ϕ(n)− Euler funcsion

$$\:\varphi\left(\mathrm{n}\right)=\varphi\left(\mathrm{n}+\mathrm{1}\right)=\varphi\left(\mathrm{n}+\mathrm{2}\right)\:\:\mathrm{n}\in\mathrm{N}\:\mathrm{n}_{\mathrm{min}} =? \\ $$$$\varphi\left(\mathrm{n}\right)−\:\mathrm{Euler}\:\mathrm{funcsion} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 150885 Answers: 0 Comments: 0

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