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IntegrationQuestion and Answers: Page 125

Question Number 117817    Answers: 2   Comments: 1

Question Number 117811    Answers: 1   Comments: 0

∫_( 0) ^( 𝛑) ln∣sinh(x)∣dx

$$\int_{\:\mathrm{0}} ^{\:\boldsymbol{\pi}} \boldsymbol{\mathrm{ln}}\mid\boldsymbol{\mathrm{sinh}}\left(\boldsymbol{\mathrm{x}}\right)\mid\boldsymbol{\mathrm{dx}} \\ $$

Question Number 117806    Answers: 4   Comments: 2

... nice calculus... i :: 1 +(4/9)+(9/(36))+((16)/(100))+...= ?? ii:: ∫_0 ^( (Ο€/2)) x^2 cot(x) dx=?? m.n.1970

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:...\:{nice}\:\:{calculus}... \\ $$$$\:\:\:\:{i}\:::\:\:\:\mathrm{1}\:+\frac{\mathrm{4}}{\mathrm{9}}+\frac{\mathrm{9}}{\mathrm{36}}+\frac{\mathrm{16}}{\mathrm{100}}+...=\:?? \\ $$$$\:\:\:\:\:{ii}::\:\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {x}^{\mathrm{2}} {cot}\left({x}\right)\:{dx}=?? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:{m}.{n}.\mathrm{1970} \\ $$$$ \\ $$

Question Number 117724    Answers: 2   Comments: 5

∫ ((sin^(βˆ’1) (x))/x^2 ) dx =?

$$\int\:\frac{\mathrm{sin}^{βˆ’\mathrm{1}} \left(\mathrm{x}\right)}{\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx}\:=? \\ $$

Question Number 117655    Answers: 0   Comments: 3

Question Number 117654    Answers: 0   Comments: 1

Question Number 117638    Answers: 2   Comments: 0

∫_0 ^1 ((2x^(12) +5x^9 )/((x^5 +x^3 +1)^3 )) dx =?

$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\mathrm{2x}^{\mathrm{12}} +\mathrm{5x}^{\mathrm{9}} }{\left(\mathrm{x}^{\mathrm{5}} +\mathrm{x}^{\mathrm{3}} +\mathrm{1}\right)^{\mathrm{3}} }\:\mathrm{dx}\:=?\: \\ $$

Question Number 117574    Answers: 1   Comments: 0

... advanced integral... Evaluate :: I := ∫_0 ^( ∞) (( 4xln(x))/(x^4 +2x^2 +4 ))dx =?? ... m.n.1970..

$$\:\:\:\:\:\:\:\:...\:{advanced}\:\:{integral}... \\ $$$$\:\:\:\:\:\: \\ $$$$\mathscr{E}{valuate}\:::\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}\::=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:\mathrm{4}{xln}\left({x}\right)}{{x}^{\mathrm{4}} +\mathrm{2}{x}^{\mathrm{2}} +\mathrm{4}\:}{dx}\:=??\: \\ $$$$\:\:\:\:\:...\:{m}.{n}.\mathrm{1970}.. \\ $$$$\: \\ $$

Question Number 117527    Answers: 1   Comments: 0

∫_( 0) ^( 1) xsec(2x)dx

$$\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \mathrm{xsec}\left(\mathrm{2x}\right)\mathrm{dx} \\ $$

Question Number 117511    Answers: 3   Comments: 0

Question Number 117496    Answers: 2   Comments: 0

∫ ((sec^2 ΞΈ tan^2 ΞΈ)/( (√(9βˆ’tan^2 ΞΈ)))) dΞΈ =?

$$\int\:\frac{\mathrm{sec}\:^{\mathrm{2}} \theta\:\mathrm{tan}\:^{\mathrm{2}} \theta}{\:\sqrt{\mathrm{9}βˆ’\mathrm{tan}\:^{\mathrm{2}} \theta}}\:\mathrm{d}\theta\:=? \\ $$

Question Number 117463    Answers: 0   Comments: 2

Question Number 117446    Answers: 2   Comments: 0

Evaluate ∫((3x^2 βˆ’5)/(x^4 +6x^2 +25))dx

$$\mathrm{Evaluate}\:\int\frac{\mathrm{3}{x}^{\mathrm{2}} βˆ’\mathrm{5}}{{x}^{\mathrm{4}} +\mathrm{6}{x}^{\mathrm{2}} +\mathrm{25}}\mathrm{d}{x} \\ $$

Question Number 117437    Answers: 2   Comments: 0

∫_0 ^∞ (dx/(a^3 +x^3 )) generaly ∫_0 ^∞ (dx/(p+x^n ))

$$\int_{\mathrm{0}} ^{\infty} \frac{{dx}}{{a}^{\mathrm{3}} +{x}^{\mathrm{3}} } \\ $$$$ \\ $$$${generaly} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{{dx}}{{p}+{x}^{{n}} } \\ $$

Question Number 117431    Answers: 0   Comments: 0

Question Number 117409    Answers: 1   Comments: 0

Question Number 117403    Answers: 1   Comments: 1

∫_0 ^1 (arc tan x)^2 dx =?

$$\:\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\left(\mathrm{arc}\:\mathrm{tan}\:\mathrm{x}\right)^{\mathrm{2}} \:\mathrm{dx}\:=? \\ $$

Question Number 117396    Answers: 3   Comments: 0

...differential equation... solve : (dy/dx)=(1/(xy+2x^2 y)) general solution =??? m.n.1970

$$\:\:\:\:\:\:\:\:...{differential}\:\:{equation}...\: \\ $$$$ \\ $$$$\:\:\:\:{solve}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\frac{{dy}}{{dx}}=\frac{\mathrm{1}}{{xy}+\mathrm{2}{x}^{\mathrm{2}} {y}} \\ $$$$\:\:\:\:\:\:\:\:\:{general}\:\:{solution}\:=??? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{m}.{n}.\mathrm{1970} \\ $$$$\: \\ $$

Question Number 117380    Answers: 1   Comments: 1

... prove that ... Ξ©=∫_0 ^( ∞) (1/(2(√x)))sin(Ο€^2 x+(1/x))dx=(1/( (√(8Ο€)))) m.n.1970

$$\:\:\:\:\:\:\:\:\:\:\:...\:\:{prove}\:\:{that}\:... \\ $$$$\:\: \\ $$$$\Omega=\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{1}}{\mathrm{2}\sqrt{{x}}}{sin}\left(\pi^{\mathrm{2}} {x}+\frac{\mathrm{1}}{{x}}\right){dx}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{8}\pi}} \\ $$$$ \\ $$$$\:\:\:\:\:\:{m}.{n}.\mathrm{1970} \\ $$

Question Number 117348    Answers: 0   Comments: 1

Question Number 117342    Answers: 2   Comments: 0

(1)∫ (tan^(βˆ’1) (x))^2 dx = ? (2) ∫ tan^(βˆ’1) ((√x)) dx =?

$$\:\left(\mathrm{1}\right)\int\:\left(\mathrm{tan}^{βˆ’\mathrm{1}} \left(\mathrm{x}\right)\right)^{\mathrm{2}} \:\mathrm{dx}\:=\:? \\ $$$$\left(\mathrm{2}\right)\:\int\:\mathrm{tan}^{βˆ’\mathrm{1}} \left(\sqrt{\mathrm{x}}\right)\:\mathrm{dx}\:=? \\ $$

Question Number 117329    Answers: 1   Comments: 0

nice math evaluate:: Ξ©=∫_0 ^( 1) ((arctan(x).ln(1βˆ’x))/(1+x^2 ))dx??? m.n.1970

$$\:\:\:\:\:\:\:\:\:{nice}\:\:{math} \\ $$$$\:\:{evaluate}:: \\ $$$$ \\ $$$$\:\:\:\: \\ $$$$\:\: \\ $$$$ \\ $$$$\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{arctan}\left({x}\right).{ln}\left(\mathrm{1}βˆ’{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}??? \\ $$$$\:\:\:\:\:\:\:\:\:{m}.{n}.\mathrm{1970} \\ $$$$ \\ $$

Question Number 117311    Answers: 2   Comments: 0

Question Number 117253    Answers: 3   Comments: 0

calculate ∫_(βˆ’βˆž) ^∞ (x^2 /((x^2 βˆ’x +1)^2 ))dx

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

Question Number 117249    Answers: 1   Comments: 0

calculate ∫_0 ^∞ (((βˆ’1)^x^2 )/(x^4 +x^2 +1))dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\left(βˆ’\mathrm{1}\right)^{\mathrm{x}^{\mathrm{2}} } }{\mathrm{x}^{\mathrm{4}} \:+\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}}\mathrm{dx}\: \\ $$

Question Number 117227    Answers: 0   Comments: 0

why every function that is Riemann integrable is not lebsgue integrable?

$${why}\:{every}\:{function}\:{that}\:{is}\:{Riemann} \\ $$$${integrable}\:{is}\:{not}\:{lebsgue}\:{integrable}? \\ $$

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