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IntegrationQuestion and Answers: Page 188

Question Number 86845    Answers: 0   Comments: 0

Question Number 86830    Answers: 2   Comments: 0

Prove that ∫_0 ^∞ ((sin x)/x)dx = (π/2)

$${Prove}\:\:{that}\:\int_{\mathrm{0}} ^{\infty} \frac{{sin}\:{x}}{{x}}{dx}\:=\:\frac{\pi}{\mathrm{2}} \\ $$

Question Number 86824    Answers: 2   Comments: 0

∫((x^6 +x^2 )/(x^8 −x^4 +1))dx

$$\int\frac{{x}^{\mathrm{6}} +{x}^{\mathrm{2}} }{{x}^{\mathrm{8}} −{x}^{\mathrm{4}} +\mathrm{1}}{dx} \\ $$

Question Number 86761    Answers: 0   Comments: 0

∫ ((x+ sin x)/(x+ cos x)) dx =

$$\int\:\:\frac{\mathrm{x}+\:\mathrm{sin}\:\mathrm{x}}{\mathrm{x}+\:\mathrm{cos}\:\mathrm{x}}\:\mathrm{dx}\:=\: \\ $$

Question Number 86728    Answers: 0   Comments: 1

∫_0 ^∞ ln(1+(b^2 /x^2 )) dx

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

Question Number 86703    Answers: 3   Comments: 6

I=∫(1/(x^4 +1))dx

$${I}=\int\frac{\mathrm{1}}{{x}^{\mathrm{4}} +\mathrm{1}}{dx} \\ $$

Question Number 86675    Answers: 1   Comments: 7

lim_(x→∞) ((∫_0 ^1 (1+x^n )^n dx))^(1/n) =?

$$\underset{{x}\rightarrow\infty} {{lim}}\sqrt[{{n}}]{\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}+{x}^{{n}} \right)^{{n}} {dx}}=? \\ $$

Question Number 86671    Answers: 1   Comments: 0

∫sin(x) arcsin(x)

$$\int{sin}\left({x}\right)\:{arcsin}\left({x}\right) \\ $$

Question Number 86646    Answers: 0   Comments: 2

∫_0 ^1 ((ln(1+x))/(x^2 +1))dx

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

Question Number 86643    Answers: 0   Comments: 2

calculate ∫_0 ^∞ ((cos(2ch(x)))/(x^2 +9))dx

$${calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{cos}\left(\mathrm{2}{ch}\left({x}\right)\right)}{{x}^{\mathrm{2}} \:+\mathrm{9}}{dx} \\ $$

Question Number 86638    Answers: 1   Comments: 0

I=∫((x^3 −2x^2 +7x−1)/((x−3)^3 (x−2)^2 ))dx

$${I}=\int\frac{{x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} +\mathrm{7}{x}−\mathrm{1}}{\left({x}−\mathrm{3}\right)^{\mathrm{3}} \left({x}−\mathrm{2}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 86627    Answers: 1   Comments: 3

Question Number 86626    Answers: 1   Comments: 2

∫(√(x^2 +4)) dx answer quick pls

$$\int\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{4}}\:\:\mathrm{dx} \\ $$$$\mathrm{answer}\:\mathrm{quick}\:\mathrm{pls} \\ $$

Question Number 86615    Answers: 1   Comments: 2

∫(√(tan x ))dx

$$\int\sqrt{{tan}\:{x}\:}{dx} \\ $$

Question Number 86613    Answers: 0   Comments: 6

∫_0 ^(1/2) ∫_0 ^(π/2) (1/(ycos(x)+1))dxdy

$$\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{1}}{{ycos}\left({x}\right)+\mathrm{1}}{dxdy} \\ $$$$ \\ $$

Question Number 86611    Answers: 1   Comments: 0

∫_1 ^e ((ln x)/(x+1))dx

$$\int_{\mathrm{1}} ^{{e}} \frac{\mathrm{ln}\:\mathrm{x}}{\mathrm{x}+\mathrm{1}}\mathrm{dx} \\ $$

Question Number 86591    Answers: 0   Comments: 0

∫_(−1) ^1 ⌊ ∣x∣+(x)^(1/3) ⌋ dx

$$\int_{−\mathrm{1}} ^{\mathrm{1}} \lfloor\:\mid{x}\mid+\sqrt[{\mathrm{3}}]{{x}}\:\rfloor\:{dx} \\ $$

Question Number 86578    Answers: 0   Comments: 2

Question Number 86576    Answers: 0   Comments: 3

∫ ((ln (1+arc sin (x^2 )))/(sin (x^2 ))) dx ?

$$\int\:\frac{\mathrm{ln}\:\left(\mathrm{1}+\mathrm{arc}\:\mathrm{sin}\:\left(\mathrm{x}^{\mathrm{2}} \right)\right)}{\mathrm{sin}\:\left(\mathrm{x}^{\mathrm{2}} \right)}\:\mathrm{dx}\:? \\ $$

Question Number 86518    Answers: 0   Comments: 1

∫ (dx/(e^(2x) −5e^x ))

$$\int\:\:\frac{\mathrm{dx}}{\mathrm{e}^{\mathrm{2x}} −\mathrm{5e}^{\mathrm{x}} } \\ $$

Question Number 86491    Answers: 2   Comments: 1

∫ ((x^2 +1)/(x^4 +1)) dx ?

$$\int\:\:\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}{\mathrm{x}^{\mathrm{4}} +\mathrm{1}}\:\mathrm{dx}\:?\: \\ $$

Question Number 86484    Answers: 2   Comments: 9

∫(x^6 /(1+x^(12) ))dx

$$\int\frac{{x}^{\mathrm{6}} }{\mathrm{1}+{x}^{\mathrm{12}} }{dx} \\ $$

Question Number 86480    Answers: 0   Comments: 1

∫_0 ^∞ (x e^(1−x) −⌊x⌋e^(1−⌊x⌋) )dx

$$\int_{\mathrm{0}} ^{\infty} \left({x}\:{e}^{\mathrm{1}−{x}} \:−\lfloor{x}\rfloor{e}^{\mathrm{1}−\lfloor{x}\rfloor} \right){dx} \\ $$

Question Number 86472    Answers: 1   Comments: 0

Question Number 86447    Answers: 0   Comments: 1

Question Number 86431    Answers: 2   Comments: 0

∫(√(x−(√(x^2 +1)) )) dx

$$\int\sqrt{{x}−\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\:}\:{dx} \\ $$

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