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IntegrationQuestion and Answers: Page 217

Question Number 71499 Answers: 1 Comments: 1

Question Number 71490 Answers: 2 Comments: 2

Question Number 71314 Answers: 2 Comments: 1

find ∫_(−1) ^1 ln((√(1+x))+(√(1−x)))dx

$${find}\:\int_{−\mathrm{1}} ^{\mathrm{1}} {ln}\left(\sqrt{\mathrm{1}+{x}}+\sqrt{\mathrm{1}−{x}}\right){dx} \\ $$

Question Number 71239 Answers: 2 Comments: 3

∫(1/(2cosx−5sinx−3))dx

$$\int\frac{\mathrm{1}}{\mathrm{2cosx}−\mathrm{5sinx}−\mathrm{3}}\mathrm{dx} \\ $$

Question Number 71220 Answers: 0 Comments: 0

Question Number 71197 Answers: 0 Comments: 0

Question Number 71175 Answers: 1 Comments: 3

∫(1/(x^2 +2016x))dx

$$\int\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} +\mathrm{2016x}}\mathrm{dx} \\ $$

Question Number 71142 Answers: 0 Comments: 1

find ∫(√(x(x+1)(x+2)))dx

$${find}\:\int\sqrt{{x}\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)}{dx} \\ $$

Question Number 71091 Answers: 0 Comments: 3

Question Number 71014 Answers: 0 Comments: 0

calculate ∫_0 ^∞ e^(−(x^2 +(1/x^2 ))) dx

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

Question Number 70909 Answers: 1 Comments: 2

Question Number 70873 Answers: 1 Comments: 0

calculate ∫∫_([1,3]^2 ) e^(−x−y) ln(2x+y)dxdy

$${calculate}\:\int\int_{\left[\mathrm{1},\mathrm{3}\right]^{\mathrm{2}} } \:\:\:{e}^{−{x}−{y}} \:{ln}\left(\mathrm{2}{x}+{y}\right){dxdy} \\ $$

Question Number 70872 Answers: 0 Comments: 1

calculate ∫∫_([1,3]^2 ) e^(−x−y) ln(2x+y)dxdy

$${calculate}\:\int\int_{\left[\mathrm{1},\mathrm{3}\right]^{\mathrm{2}} } \:\:\:{e}^{−{x}−{y}} \:{ln}\left(\mathrm{2}{x}+{y}\right){dxdy} \\ $$

Question Number 70871 Answers: 0 Comments: 1

calculate f(x)=∫_(−∞) ^(+∞) ((cos(x(1+t^2 )))/(1+t^2 ))dt with x≥0

$$\:{calculate}\:{f}\left({x}\right)=\int_{−\infty} ^{+\infty} \:\frac{{cos}\left({x}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)\right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt}\:{with}\:{x}\geqslant\mathrm{0} \\ $$

Question Number 70870 Answers: 0 Comments: 4

let f(x)=∫_(−∞) ^(+∞) (dt/((t^2 −2t +x^2 )^4 )) with ∣x∣>1 and n integr natural 1)find a explicit form for f(x) 2) determine also g(x)=∫_(−∞) ^(+∞) (dt/((t^2 −2t +x^2 )^5 )) 3)find the values of integrals ∫_(−∞) ^(+∞) (dt/((t^2 −2t +3)^4 )) and ∫_(−∞) ^(+∞) (dt/((t^2 −2t +3)^5 ))

$${let}\:{f}\left({x}\right)=\int_{−\infty} ^{+\infty} \:\:\frac{{dt}}{\left({t}^{\mathrm{2}} −\mathrm{2}{t}\:+{x}^{\mathrm{2}} \right)^{\mathrm{4}} }\:\:{with}\:\:\mid{x}\mid>\mathrm{1} \\ $$$${and}\:{n}\:{integr}\:{natural} \\ $$$$\left.\mathrm{1}\right){find}\:{a}\:{explicit}\:{form}\:{for}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{also}\:{g}\left({x}\right)=\int_{−\infty} ^{+\infty} \:\:\frac{{dt}}{\left({t}^{\mathrm{2}} −\mathrm{2}{t}\:+{x}^{\mathrm{2}} \right)^{\mathrm{5}} } \\ $$$$\left.\mathrm{3}\right){find}\:{the}\:{values}\:{of}\:{integrals}\: \\ $$$$\int_{−\infty} ^{+\infty} \:\frac{{dt}}{\left({t}^{\mathrm{2}} −\mathrm{2}{t}\:+\mathrm{3}\right)^{\mathrm{4}} }\:\:{and}\:\int_{−\infty} ^{+\infty} \:\frac{{dt}}{\left({t}^{\mathrm{2}} −\mathrm{2}{t}\:+\mathrm{3}\right)^{\mathrm{5}} } \\ $$

Question Number 70842 Answers: 0 Comments: 1