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Question Number 57234 Answers: 0 Comments: 0

let tbe fraction F(x)=(1/(x^n −1)) with n from n and n≥2 1) find the poles of F and decompose it inside C(x) 2)decompose F(x)inside R(x) 3) calculate ∫_2 ^3 F(x)dx .

$${let}\:{tbe}\:{fraction}\:{F}\left({x}\right)=\frac{\mathrm{1}}{{x}^{{n}} −\mathrm{1}}\:\:{with}\:{n}\:{from}\:{n}\:{and}\:{n}\geqslant\mathrm{2} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{poles}\:{of}\:{F}\:{and}\:{decompose}\:{it}\:{inside}\:{C}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){decompose}\:{F}\left({x}\right){inside}\:{R}\left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{2}} ^{\mathrm{3}} {F}\left({x}\right){dx}\:. \\ $$

Question Number 57233 Answers: 0 Comments: 1

find the value of ∫_0 ^(+∞) (x^4 /((1+x^2 +x^4 )^2 ))dx

$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{+\infty} \:\:\frac{{x}^{\mathrm{4}} }{\left(\mathrm{1}+{x}^{\mathrm{2}} \:+{x}^{\mathrm{4}} \right)^{\mathrm{2}} }{dx} \\ $$

Question Number 57232 Answers: 0 Comments: 1

decompose tbe fraction F(x)=(1/(x^n (x+1))) with n integr natural.

$${decompose}\:{tbe}\:{fraction}\:{F}\left({x}\right)=\frac{\mathrm{1}}{{x}^{{n}} \left({x}+\mathrm{1}\right)}\:\:{with}\:{n}\:{integr}\:{natural}. \\ $$

Question Number 57231 Answers: 0 Comments: 1

find tbe value of ∫_(−∞) ^(+∞) ((x−3)/((x^2 +1)(x^2 −x +2)^2 )) dx

$${find}\:{tbe}\:{value}\:{of}\:\int_{−\infty} ^{+\infty} \:\:\frac{{x}−\mathrm{3}}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)\left({x}^{\mathrm{2}} −{x}\:+\mathrm{2}\right)^{\mathrm{2}} }\:{dx} \\ $$

Question Number 57230 Answers: 0 Comments: 0

1) find ∫ (dx/(x^2 (x+1)^3 (x^2 +1))) 2) calculate ∫_1 ^(√3) (dx/(x^2 (x+1)^3 (x^2 +1)))

$$\left.\mathrm{1}\right)\:{find}\:\int\:\:\frac{{dx}}{{x}^{\mathrm{2}} \left({x}+\mathrm{1}\right)^{\mathrm{3}} \left({x}^{\mathrm{2}} \:+\mathrm{1}\right)} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{1}} ^{\sqrt{\mathrm{3}}} \:\:\:\:\:\frac{{dx}}{{x}^{\mathrm{2}} \left({x}+\mathrm{1}\right)^{\mathrm{3}} \left({x}^{\mathrm{2}} \:+\mathrm{1}\right)} \\ $$

Question Number 57229 Answers: 1 Comments: 1

give ∫_0 ^1 (x^5 /(x^3 +1)) dx at form of serie

$${give}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{x}^{\mathrm{5}} }{{x}^{\mathrm{3}} \:+\mathrm{1}}\:{dx}\:{at}\:{form}\:{of}\:{serie} \\ $$

Question Number 57198 Answers: 0 Comments: 2

Question Number 57175 Answers: 0 Comments: 5

Question Number 57174 Answers: 1 Comments: 0

Question Number 57173 Answers: 0 Comments: 0

Question Number 57164 Answers: 1 Comments: 0

2x+1+x^2 −x^3 +x^4 −x^5 −.....=((13)/6) solved equation. ∣x∣<1

$$\mathrm{2}\boldsymbol{\mathrm{x}}+\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\boldsymbol{\mathrm{x}}^{\mathrm{3}} +\boldsymbol{\mathrm{x}}^{\mathrm{4}} −\boldsymbol{\mathrm{x}}^{\mathrm{5}} −.....=\frac{\mathrm{13}}{\mathrm{6}} \\ $$$$\boldsymbol{\mathrm{solved}}\:\:\boldsymbol{\mathrm{equation}}. \\ $$$$\mid\boldsymbol{\mathrm{x}}\mid<\mathrm{1} \\ $$

Question Number 57163 Answers: 0 Comments: 0

Question Number 57140 Answers: 1 Comments: 0

∫_( 0) ^1 (√((1+x)(1+x^3 ))) dx ≤ ((15)/8)

$$\underset{\:\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\sqrt{\left(\mathrm{1}+{x}\right)\left(\mathrm{1}+{x}^{\mathrm{3}} \right)}\:{dx}\:\leqslant\:\frac{\mathrm{15}}{\mathrm{8}} \\ $$

Question Number 57138 Answers: 1 Comments: 1

The value of the integral ∫_( 0) ^π (1/(a^2 −2a cos x+1)) dx (a >1) is

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{integral} \\ $$$$\underset{\:\mathrm{0}} {\overset{\pi} {\int}}\:\:\:\frac{\mathrm{1}}{{a}^{\mathrm{2}} −\mathrm{2}{a}\:\mathrm{cos}\:{x}+\mathrm{1}}\:{dx}\:\:\left({a}\:>\mathrm{1}\right)\:\:\mathrm{is} \\ $$

Question Number 57136 Answers: 1 Comments: 0

∫_a ^b ((f(x))/(f(x)+f(a+b−x))) dx =

$$\underset{{a}} {\overset{{b}} {\int}}\:\:\frac{{f}\left({x}\right)}{{f}\left({x}\right)+{f}\left({a}+{b}−{x}\right)}\:{dx}\:= \\ $$

Question Number 57127 Answers: 0 Comments: 24

{cos1°}+{cos2°}+{cos3°}+....+{cos270}=?

$$\left\{\boldsymbol{\mathrm{cos}}\mathrm{1}°\right\}+\left\{\boldsymbol{\mathrm{cos}}\mathrm{2}°\right\}+\left\{\boldsymbol{\mathrm{cos}}\mathrm{3}°\right\}+....+\left\{\boldsymbol{\mathrm{cos}}\mathrm{270}\right\}=? \\ $$

Question Number 57124 Answers: 1 Comments: 3

Question Number 59160 Answers: 0 Comments: 0

let f(x) =∫_0 ^∞ ((cos(xcosθ))/(x^2 +θ^2 )) dθ and g(x) =∫_0 ^∞ ((sin(xcosθ))/(x^2 +θ^2 )) dθ 1) find a explicit form of f(x) and g(x) 2) find the value of ∫_0 ^∞ ((cos(2cosθ))/(4+θ^2 )) dθ and ∫_0 ^∞ ((sin(2cosθ))/(4+θ^2 )) dθ 3) let u_n =f(n^2 ) study the serie Σ u_n

$${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({xcos}\theta\right)}{{x}^{\mathrm{2}} \:+\theta^{\mathrm{2}} }\:{d}\theta\:\:\:\:\:\:{and}\:\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{sin}\left({xcos}\theta\right)}{{x}^{\mathrm{2}} \:+\theta^{\mathrm{2}} }\:{d}\theta \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right)\:{and}\:{g}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{cos}\left(\mathrm{2}{cos}\theta\right)}{\mathrm{4}+\theta^{\mathrm{2}} }\:{d}\theta\:\:{and}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{sin}\left(\mathrm{2}{cos}\theta\right)}{\mathrm{4}+\theta^{\mathrm{2}} }\:{d}\theta \\ $$$$\left.\mathrm{3}\right)\:{let}\:{u}_{{n}} ={f}\left({n}^{\mathrm{2}} \right)\:\:\:{study}\:\:{the}\:{serie}\:\Sigma\:{u}_{{n}} \\ $$

Question Number 57115 Answers: 0 Comments: 0