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IntegrationQuestion and Answers: Page 294

Question Number 36649 Answers: 1 Comments: 4

∫ (1/(x^4 +1)) dx

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

Question Number 36643 Answers: 2 Comments: 1

∫ (x/(x^4 +x^2 +1)) dx = ?

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

Question Number 36633 Answers: 0 Comments: 1

calculate ∫_0 ^1 arctan(x^2 +x+1)dx

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

Question Number 36613 Answers: 1 Comments: 5

Question Number 36597 Answers: 2 Comments: 2

∫(dx/(x^(2/3) (1+x^(2/3) ))) = ?

$$\int\frac{\mathrm{d}{x}}{{x}^{\frac{\mathrm{2}}{\mathrm{3}}} \left(\mathrm{1}+{x}^{\frac{\mathrm{2}}{\mathrm{3}}} \right)}\:=\:? \\ $$

Question Number 36659 Answers: 1 Comments: 3

∫ (1/(sin^4 x+cos^4 x)) dx

$$\int\:\frac{\mathrm{1}}{\mathrm{sin}\:^{\mathrm{4}} {x}+\mathrm{cos}\:^{\mathrm{4}} {x}}\:{dx} \\ $$

Question Number 36595 Answers: 2 Comments: 0

∫ ((x dx)/(√(1+x^2 +(√((1+x^2 )^3 ))))) = ?

$$\int\:\frac{{x}\:{dx}}{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} +\sqrt{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{3}} }}}\:=\:? \\ $$

Question Number 36547 Answers: 3 Comments: 0

∫((5x^4 +4x^5 )/((x^5 +x+1)^2 ))

$$\int\frac{\mathrm{5}{x}^{\mathrm{4}} +\mathrm{4}{x}^{\mathrm{5}} }{\left({x}^{\mathrm{5}} +{x}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 36546 Answers: 0 Comments: 0

∫(((x−1))/((x+1)(√(x^3 +x^2 +x))))dx

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

Question Number 36545 Answers: 2 Comments: 6

∫((2x+1)/((x^2 +4x+1)^(3/2) ))dx

$$\int\frac{\mathrm{2}{x}+\mathrm{1}}{\left({x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{1}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} }{dx} \\ $$

Question Number 36544 Answers: 1 Comments: 0

∫(dx/(tanx+cotx+secx+cosecx))

$$\int\frac{{dx}}{{tanx}+{cotx}+{secx}+{cosecx}} \\ $$

Question Number 36543 Answers: 0 Comments: 0

∫cot^(−1) (x^2 +x+1) dx

$$\int{cot}^{−\mathrm{1}} \left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)\:{dx} \\ $$

Question Number 36541 Answers: 0 Comments: 1

∫(x+(√(1+x^2 )) )^n dx

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

Question Number 36538 Answers: 0 Comments: 1

∫(dx/((a+bx^2 )(√(b−ax^2 ))))

$$\int\frac{{dx}}{\left({a}+{bx}^{\mathrm{2}} \right)\sqrt{{b}−{ax}^{\mathrm{2}} \:}}\:\: \\ $$

Question Number 36537 Answers: 0 Comments: 3

Question Number 36536 Answers: 0 Comments: 0

Question Number 36535 Answers: 0 Comments: 0

∫(dx/(secx+cosecx))

$$\int\frac{{dx}}{{secx}+{cosecx}} \\ $$

Question Number 36534 Answers: 0 Comments: 0

Question Number 36533 Answers: 0 Comments: 0

Question Number 36491 Answers: 2 Comments: 0

Question Number 36459 Answers: 2 Comments: 0

∫ e^(tan θ) (sec θ −sin θ) dθ = ?

$$\int\:\mathrm{e}^{\mathrm{tan}\:\theta} \left(\mathrm{sec}\:\theta\:−\mathrm{sin}\:\theta\right)\:\mathrm{d}\theta\:=\:? \\ $$

Question Number 36444 Answers: 0 Comments: 11

∫ (dx/((2x−7)(√((x−3)(x−4))))) = ?

$$\int\:\frac{\mathrm{d}{x}}{\left(\mathrm{2}{x}−\mathrm{7}\right)\sqrt{\left({x}−\mathrm{3}\right)\left({x}−\mathrm{4}\right)}}\:=\:? \\ $$

Question Number 36441 Answers: 1 Comments: 1

find ∫ (e^(tanx) /(cos^2 x))dx

$${find}\:\:\int\:\:\:\frac{{e}^{{tanx}} }{{cos}^{\mathrm{2}} {x}}{dx} \\ $$

Question Number 36440 Answers: 0 Comments: 0

find ∫ (dx/((3+x^2 )^(1/3) ))

$${find}\:\int\:\:\:\:\frac{{dx}}{\left(\mathrm{3}+{x}^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{3}}} } \\ $$

Question Number 36439 Answers: 1 Comments: 1

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

$${calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:\:\frac{{sin}\left(\mathrm{2}{x}\right)}{\mathrm{2}\:+{cosx}}{dx} \\ $$

Question Number 36438 Answers: 1 Comments: 3

let F(x) =∫_x ^(1/x) ((arctan(t))/t)dt 1) calculate (dF/dx)(x) 2) find F(x).

$${let}\:{F}\left({x}\right)\:=\int_{{x}} ^{\frac{\mathrm{1}}{{x}}} \:\:\frac{{arctan}\left({t}\right)}{{t}}{dt} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\:\frac{{dF}}{{dx}}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{F}\left({x}\right). \\ $$

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