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IntegrationQuestion and Answers: Page 199

Question Number 76920 Answers: 0 Comments: 1

how can i solve ∫ ((sin x dx)/(x^2 e^x )) ? can using elementary calculus?

$${how}\:{can}\:{i}\:{solve}\: \\ $$$$\int\:\frac{\mathrm{sin}\:{x}\:{dx}}{{x}^{\mathrm{2}} \:{e}^{{x}} }\:?\:{can}\:{using}\:{elementary} \\ $$$${calculus}? \\ $$

Question Number 76913 Answers: 1 Comments: 0

Question Number 76910 Answers: 1 Comments: 1

Question Number 76892 Answers: 3 Comments: 0

Calculate ∫ ((√(9−x^2 ))/x^6 ) dx .

$$\mathcal{C}{alculate}\:\int\:\frac{\sqrt{\mathrm{9}−{x}^{\mathrm{2}} }}{{x}^{\mathrm{6}} }\:{dx}\:. \\ $$

Question Number 76826 Answers: 1 Comments: 0

Question Number 76808 Answers: 1 Comments: 3

∫(1/(√(x^3 +1)))dx

$$\int\frac{\mathrm{1}}{\sqrt{{x}^{\mathrm{3}} +\mathrm{1}}}{dx} \\ $$

Question Number 76782 Answers: 1 Comments: 0

calculate ∫_0 ^∞ e^(−x) ((sin(x^2 ))/x^2 )dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{x}} \:\:\frac{{sin}\left({x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 76781 Answers: 0 Comments: 2

find ∫_0 ^∞ ((1−e^(−x^2 ) )/x^2 )dx

$${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{1}−{e}^{−{x}^{\mathrm{2}} } }{{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 76780 Answers: 0 Comments: 1

find A=∫_(−∞) ^(+∞) x e^(−x^2 ) arctan(x−(1/x))dx

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

Question Number 76779 Answers: 0 Comments: 1

calculate ∫_0 ^π ((x^2 cosx)/(3+sin^2 x))dx

$${calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{{x}^{\mathrm{2}} {cosx}}{\mathrm{3}+{sin}^{\mathrm{2}} {x}}{dx} \\ $$

Question Number 76688 Answers: 1 Comments: 0

calculate ∫ (1/(lnx))+ ln(lnx) dx .

$${calculate}\:\int\:\frac{\mathrm{1}}{{lnx}}+\:{ln}\left({lnx}\right)\:{dx}\:. \\ $$

Question Number 76669 Answers: 0 Comments: 2

Question Number 76664 Answers: 0 Comments: 1

∫_0 ^(+∞) ((t ln(t))/((t^2 +1)^2 )) dt

$$\int_{\mathrm{0}} ^{+\infty} \frac{{t}\:{ln}\left({t}\right)}{\left({t}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }\:{dt} \\ $$

Question Number 76661 Answers: 1 Comments: 0

calculate ∫ ((x^2 −2)/((x^4 +5x^2 +4) arctan (((x^2 +2)/x)))) dx

$${calculate}\:\int\:\frac{{x}^{\mathrm{2}} −\mathrm{2}}{\left({x}^{\mathrm{4}} +\mathrm{5}{x}^{\mathrm{2}} +\mathrm{4}\right)\:{arc}\mathrm{tan}\:\left(\frac{{x}^{\mathrm{2}} +\mathrm{2}}{{x}}\right)}\:{dx}\: \\ $$

Question Number 76615 Answers: 2 Comments: 0

∫sec^3 x dx

$$\int{sec}^{\mathrm{3}} {x}\:{dx} \\ $$

Question Number 76572 Answers: 1 Comments: 0

how do you find the least value of x^2 +2xy+3y^2 −6x−2y using the concepts of algebra or calculus?

$${how}\:{do}\:{you}\:{find}\:{the}\:{least}\:{value}\:{of}\:{x}^{\mathrm{2}} \\ $$$$+\mathrm{2}{xy}+\mathrm{3}{y}^{\mathrm{2}} −\mathrm{6}{x}−\mathrm{2}{y}\:{using}\:{the}\: \\ $$$${concepts}\:{of}\:{algebra}\:{or}\:{calculus}?\: \\ $$

Question Number 76469 Answers: 2 Comments: 3

∫cothx dx

$$\int{cothx}\:{dx} \\ $$

Question Number 76468 Answers: 1 Comments: 2

∫((1−x^2 −8x+1)/(x^4 −x^3 −x+1))dx

$$\int\frac{\mathrm{1}−{x}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{1}}{{x}^{\mathrm{4}} −{x}^{\mathrm{3}} −{x}+\mathrm{1}}{dx} \\ $$

Question Number 76467 Answers: 1 Comments: 0

∫(dx/((√(e^(2x) −4))(sec^(−1) ((e^x /4)))))

$$\int\frac{{dx}}{\sqrt{{e}^{\mathrm{2}{x}} −\mathrm{4}}\left({sec}^{−\mathrm{1}} \left(\frac{{e}^{{x}} }{\mathrm{4}}\right)\right)} \\ $$

Question Number 76465 Answers: 1 Comments: 0

∫e^(−x) (−e^(−3x) +5e^(−2x) −6)sin(2e^(−x) )dx

$$\int{e}^{−{x}} \left(−{e}^{−\mathrm{3}{x}} +\mathrm{5}{e}^{−\mathrm{2}{x}} −\mathrm{6}\right){sin}\left(\mathrm{2}{e}^{−{x}} \right){dx} \\ $$

Question Number 76462 Answers: 1 Comments: 4

∫cos3x e^(−2x) dx

$$\int{cos}\mathrm{3}{x}\:{e}^{−\mathrm{2}{x}} {dx} \\ $$

Question Number 76442 Answers: 1 Comments: 0

Question Number 76424 Answers: 1 Comments: 1

how to calculate ∫(√(x/(√(x/(√(x/(√(...)))))))) dx ?

$${how}\:{to}\:{calculate}\:\int\sqrt{\frac{{x}}{\sqrt{\frac{{x}}{\sqrt{\frac{{x}}{\sqrt{...}}}}}}}\:\:{dx}\:? \\ $$

Question Number 76360 Answers: 0 Comments: 1

calculate ∫_1 ^∞ (dx/(x^3 (x^2 −2x+3)))

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

Question Number 76359 Answers: 0 Comments: 1

calculate ∫_(−∞) ^∞ (dx/((x^2 −3x+7)^2 ))

$${calculate}\:\int_{−\infty} ^{\infty} \:\:\frac{{dx}}{\left({x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{7}\right)^{\mathrm{2}} } \\ $$

Question Number 76356 Answers: 0 Comments: 1

find f(x) =∫ (dt/(√(t^2 −xt +1))) with x real.

$${find}\:{f}\left({x}\right)\:=\int\:\:\frac{{dt}}{\sqrt{{t}^{\mathrm{2}} −{xt}\:+\mathrm{1}}}\:\:{with}\:{x}\:{real}. \\ $$

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