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AllQuestion and Answers: Page 1409

Question Number 69665 Answers: 1 Comments: 1

Question Number 69662 Answers: 1 Comments: 0

prove that ((2x^3 −x^2 −2x+1)/(x^3 +1)) + ((x^3 +1)/(x^4 −2x^3 +3x^2 −2x+1)) = 2

$${prove}\:{that} \\ $$$$ \\ $$$$\frac{\mathrm{2}{x}^{\mathrm{3}} −{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{1}}{{x}^{\mathrm{3}} +\mathrm{1}}\:+\:\frac{{x}^{\mathrm{3}} +\mathrm{1}}{{x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{3}} +\mathrm{3}{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{1}}\:=\:\mathrm{2} \\ $$

Question Number 69645 Answers: 1 Comments: 0

Question Number 69644 Answers: 2 Comments: 0

Question Number 69643 Answers: 1 Comments: 0

Question Number 69641 Answers: 0 Comments: 0

Solve arctg(1−x) + (1/(arcctg(1+x))) = (𝛑/4)

$$\boldsymbol{{Solve}}\:\:\boldsymbol{{arctg}}\left(\mathrm{1}−\boldsymbol{{x}}\right)\:+\:\frac{\mathrm{1}}{\boldsymbol{{arcctg}}\left(\mathrm{1}+\boldsymbol{{x}}\right)}\:=\:\frac{\boldsymbol{\pi}}{\mathrm{4}} \\ $$

Question Number 69637 Answers: 1 Comments: 0

...now try this one: ∫(dx/(x^(1/2) −x^(1/3) −x^(1/6) ))=

$$...\mathrm{now}\:\mathrm{try}\:\mathrm{this}\:\mathrm{one}: \\ $$$$\int\frac{{dx}}{{x}^{\mathrm{1}/\mathrm{2}} −{x}^{\mathrm{1}/\mathrm{3}} −{x}^{\mathrm{1}/\mathrm{6}} }= \\ $$

Question Number 69623 Answers: 1 Comments: 0

∫(1/((√x) + (x)^(1/3) )) dx

$$\int\frac{\mathrm{1}}{\sqrt{{x}}\:+\:\sqrt[{\mathrm{3}}]{{x}}}\:{dx} \\ $$

Question Number 69616 Answers: 0 Comments: 4

Question Number 69606 Answers: 0 Comments: 0

Question Number 69603 Answers: 1 Comments: 0

∫ x^3 arcsinxdx

$$\int\:{x}^{\mathrm{3}} {arcsinxdx} \\ $$

Question Number 69597 Answers: 1 Comments: 1

Question Number 69594 Answers: 1 Comments: 0

Question Number 69593 Answers: 1 Comments: 2

Question Number 69576 Answers: 1 Comments: 1

∫_(−2) ^( 2) (x^3 cos(x/2)+(1/2))(√(4−x^2 ))dx

$$\int_{−\mathrm{2}} ^{\:\mathrm{2}} \left({x}^{\mathrm{3}} {cos}\frac{{x}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}}\right)\sqrt{\mathrm{4}−{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 69574 Answers: 1 Comments: 0

Question Number 69573 Answers: 0 Comments: 1

Question Number 69572 Answers: 1 Comments: 0

Question Number 69571 Answers: 1 Comments: 0

Question Number 69570 Answers: 0 Comments: 0

Question Number 69569 Answers: 2 Comments: 0

Question Number 69568 Answers: 1 Comments: 3

Question Number 69567 Answers: 0 Comments: 2

Question Number 69566 Answers: 1 Comments: 0

Question Number 69565 Answers: 0 Comments: 0

Question Number 69564 Answers: 0 Comments: 3

let f(a) =∫_0 ^∞ (dx/(x^4 −2x^2 +a)) with a real and a>1 1) determine a explicit form for f(a) 2) calculate g(a) =∫_0 ^∞ (dx/((x^4 −2x^2 +a)^2 )) 3) find the values of integrals ∫_0 ^∞ (dx/(x^4 −2x^2 +3)) and ∫_0 ^∞ (dx/((x^4 −2x^2 +3)^2 ))

$${let}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{{x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{2}} \:+{a}}\:\:\:{with}\:{a}\:{real}\:{and}\:{a}>\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:{for}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:\:{calculate}\:{g}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left({x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{2}} +{a}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{values}\:{of}\:{integrals}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{{x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{2}} \:+\mathrm{3}} \\ $$$${and}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left({x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{2}} \:+\mathrm{3}\right)^{\mathrm{2}} } \\ $$$$ \\ $$$$ \\ $$

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