Question and Answers Forum

1) explicite f(a) =∫_(−∞) ^(+∞) ((arctan(a+x))/(x^2 +4))dx 1) 1)calculate ∫_(−∞) ^(+∞) ((arctan(1+x))/(x^2 +4))dx and ∫_(−∞) ^(+∞) ((arctan(3+x))/(x^2 +4))dx

$$\left.\mathrm{1}\right)\:{explicite}\:{f}\left({a}\right)\:=\int_{−\infty} ^{+\infty} \:\frac{{arctan}\left({a}+{x}\right)}{{x}^{\mathrm{2}} \:+\mathrm{4}}{dx} \\ $$$$\left.\mathrm{1}\left.\right)\:\mathrm{1}\right){calculate}\:\int_{−\infty} ^{+\infty} \:\:\frac{{arctan}\left(\mathrm{1}+{x}\right)}{{x}^{\mathrm{2}} +\mathrm{4}}{dx} \\ $$$${and}\:\int_{−\infty} ^{+\infty} \:\frac{{arctan}\left(\mathrm{3}+{x}\right)}{{x}^{\mathrm{2}} +\mathrm{4}}{dx} \\ $$

Question Number 116311 Answers: 3 Comments: 0

∫_0 ^(π/3) ((sin 2x)/((sin x)^(4/3) )) dx

$$\:\:\:\:\:\:\:\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{3}}} {\int}}\:\frac{\mathrm{sin}\:\mathrm{2x}}{\left(\mathrm{sin}\:\mathrm{x}\right)^{\frac{\mathrm{4}}{\mathrm{3}}} }\:\mathrm{dx}\: \\ $$$$ \\ $$

Question Number 116299 Answers: 0 Comments: 0

... advanced math ... evaluate that : Ω=∫_0 ^( 1) [(1/(ln(x))) +(1/(1−x)) ]^2 dx=??? m.n

$$\:\:\:...\:\:{advanced}\:\:{math}\:... \\ $$$$\:\:\:\:\:\:\:{evaluate}\:{that}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\mathrm{1}} \left[\frac{\mathrm{1}}{{ln}\left({x}\right)}\:+\frac{\mathrm{1}}{\mathrm{1}−{x}}\:\right]^{\mathrm{2}} {dx}=??? \\ $$$$\:\:\:\:\:\:\:{m}.{n} \\ $$

Question Number 116272 Answers: 1 Comments: 0

∫_0 ^(π/2) ln(x^2 +ln^2 (cos(x)))dx=πln(ln(2)) posted Quation not solved yet i hop someon Giv idea for this one thank you

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left({x}^{\mathrm{2}} +{ln}^{\mathrm{2}} \left({cos}\left({x}\right)\right)\right){dx}=\pi{ln}\left({ln}\left(\mathrm{2}\right)\right) \\ $$$${posted}\:{Quation}\: \\ $$$${not}\:{solved}\:{yet}\:{i}\:{hop}\:{someon}\:{Giv}\:{idea}\:{for} \\ $$$${this}\:{one}\:{thank}\:{you} \\ $$

Question Number 116250 Answers: 0 Comments: 0

1)explicite U_n =∫_0 ^∞ e^(−n[x]) cos(3[x])dx 2) calculate lim_(n→+∞) U_n 3)find nsture of Σ U_n

$$\left.\mathrm{1}\right)\mathrm{explicite}\:\mathrm{U}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\infty} \:\mathrm{e}^{−\mathrm{n}\left[\mathrm{x}\right]} \mathrm{cos}\left(\mathrm{3}\left[\mathrm{x}\right]\right)\mathrm{dx} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{calculate}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\mathrm{U}_{\mathrm{n}} \\ $$$$\left.\mathrm{3}\right)\mathrm{find}\:\mathrm{nsture}\:\mathrm{of}\:\Sigma\:\mathrm{U}_{\mathrm{n}} \\ $$

Question Number 116249 Answers: 0 Comments: 0

find ∫_0 ^1 ((arctan(x^2 +3))/(x^2 +3))dx

$$\mathrm{find}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{\mathrm{arctan}\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{3}\right)}{\mathrm{x}^{\mathrm{2}} +\mathrm{3}}\mathrm{dx} \\ $$

Question Number 116248 Answers: 0 Comments: 0

calculate ∫_(−∞) ^∞ ((arctan(2+x^2 ))/(x^2 −x +1))dx

$$\mathrm{calculate}\:\int_{−\infty} ^{\infty} \:\:\frac{\mathrm{arctan}\left(\mathrm{2}+\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{x}^{\mathrm{2}} −\mathrm{x}\:+\mathrm{1}}\mathrm{dx} \\ $$

Question Number 116247 Answers: 0 Comments: 0

find the value of I =∫_0 ^∞ ((ch(cos(2x)))/(x^2 +9))dx and J =∫_0 ^∞ ((cos(ch(2x)))/(x^2 +9))dx

$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\:\mathrm{I}\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{ch}\left(\mathrm{cos}\left(\mathrm{2x}\right)\right)}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{9}}\mathrm{dx}\:\mathrm{and} \\ $$$$\mathrm{J}\:=\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{cos}\left(\mathrm{ch}\left(\mathrm{2x}\right)\right)}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{9}}\mathrm{dx} \\ $$

Question Number 116245 Answers: 3 Comments: 0

calculate ∫_1 ^∞ (dx/((2x^2 −1)^5 ))

$$\mathrm{calculate}\:\:\int_{\mathrm{1}} ^{\infty} \:\frac{\mathrm{dx}}{\left(\mathrm{2x}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{5}} } \\ $$

Question Number 116237 Answers: 2 Comments: 0

∫ (√(5cos^2 x+4)) dx ?

$$\int\:\sqrt{\mathrm{5cos}\:^{\mathrm{2}} \mathrm{x}+\mathrm{4}}\:\mathrm{dx}\:? \\ $$

Question Number 116231 Answers: 1 Comments: 0

∫ sec x tan x (√(tan^2 x−3)) dx ?

$$\int\:\mathrm{sec}\:\mathrm{x}\:\mathrm{tan}\:\mathrm{x}\:\sqrt{\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}−\mathrm{3}}\:\mathrm{dx}\:? \\ $$

Question Number 116216 Answers: 1 Comments: 0

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

$$\underset{\mathrm{0}} {\overset{\pi} {\int}}\:\frac{\mathrm{ln}\:\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\mathrm{x}\right)}{\mathrm{cos}\:\mathrm{x}}\:\mathrm{dx}\:? \\ $$

Question Number 116162 Answers: 1 Comments: 0

Σ_(n=0) ^∞ ((2n+1)/(16^n (n^2 +3n+2))) (((2n)),(n) )^2 =(8/(3π)) m.n.july 1970.

$$\:\: \\ $$$$ \\ $$$$\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{2}{n}+\mathrm{1}}{\mathrm{16}^{{n}} \left({n}^{\mathrm{2}} +\mathrm{3}{n}+\mathrm{2}\right)}\:\begin{pmatrix}{\mathrm{2}{n}}\\{{n}}\end{pmatrix}^{\mathrm{2}} \:=\frac{\mathrm{8}}{\mathrm{3}\pi}\: \\ $$$$ \\ $$$${m}.{n}.{july}\:\mathrm{1970}. \\ $$$$\: \\ $$

Question Number 116196 Answers: 6 Comments: 0

please solve : ∫_0 ^( (π/4)) tan^9 (x)dx =???

$$\:\:\:\:\:{please}\:{solve}\:: \\ $$$$\:\:\: \\ $$$$\:\:\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} {tan}^{\mathrm{9}} \left({x}\right){dx}\:=??? \\ $$

Question Number 116112 Answers: 2 Comments: 0

show that ∫_( 0) ^( ∞) ((lnx)/(1+x^2 ))dx = 0

$$\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}}\: \\ $$$$\int_{\:\mathrm{0}} ^{\:\infty} \frac{\boldsymbol{\mathrm{lnx}}}{\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\boldsymbol{\mathrm{dx}}\:=\:\mathrm{0} \\ $$$$ \\ $$

Question Number 116123 Answers: 0 Comments: 0

Study according to the values of the real α the convergence of the integral ∫_α ^(+∞) ((ln∣x∣)/( ((x(x+1)))^(1/3) ))dx

$$ \\ $$$$\mathrm{Study}\:\mathrm{according}\:\mathrm{to}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\: \\ $$$$\mathrm{the}\:\mathrm{real}\:\alpha\:\mathrm{the}\:\mathrm{convergence}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{integral}\:\:\int_{\alpha} ^{+\infty} \frac{{ln}\mid{x}\mid}{\:\sqrt[{\mathrm{3}}]{{x}\left({x}+\mathrm{1}\right)}}{dx} \\ $$

Question Number 116098 Answers: 0 Comments: 0

1)calculate f(x)=∫_0 ^(2π) (dθ/(x^2 −2x cosθ +1)) 0<θ<(π/2) 2)explicite ∫_0 ^(2π) ((cosθ)/((x^2 −2xcosθ +1)^2 ))dθ

$$\left.\mathrm{1}\right)\mathrm{calculate}\:\mathrm{f}\left(\mathrm{x}\right)=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\frac{\mathrm{d}\theta}{\mathrm{x}^{\mathrm{2}} −\mathrm{2x}\:\mathrm{cos}\theta\:+\mathrm{1}}\:\:\:\:\mathrm{0}<\theta<\frac{\pi}{\mathrm{2}} \\ $$$$\left.\mathrm{2}\right)\mathrm{explicite}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{\mathrm{cos}\theta}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{2xcos}\theta\:+\mathrm{1}\right)^{\mathrm{2}} }\mathrm{d}\theta \\ $$

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