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IntegrationQuestion and Answers: Page 186

Question Number 84570 Answers: 1 Comments: 1

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

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

Question Number 84569 Answers: 1 Comments: 0

find ∫ (dx/(1+tan^4 x))

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

Question Number 84566 Answers: 0 Comments: 0

Question Number 84561 Answers: 1 Comments: 0

∫_0 ^∞ ∫_0 ^∞ ((cos(x−y)−cos(x))/(xy))dx dy

$$\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\infty} \frac{{cos}\left({x}−{y}\right)−{cos}\left({x}\right)}{{xy}}{dx}\:{dy} \\ $$

Question Number 84557 Answers: 0 Comments: 1

Question Number 84556 Answers: 1 Comments: 1

∫ sin^(−1) (((2x+2)/(√(4x^2 +8x+13)))) dx

$$\int\:\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{2x}+\mathrm{2}}{\sqrt{\mathrm{4x}^{\mathrm{2}} +\mathrm{8x}+\mathrm{13}}}\right)\:\mathrm{dx} \\ $$

Question Number 84549 Answers: 1 Comments: 0

Question Number 84505 Answers: 0 Comments: 1

2)calculate I(ξ) =∫_ξ ^1 (dx/(√(1+ξx^2 −(√(1−ξx^2 ))))) 1)find lim_(ξ→0) I(ξ)

$$\left.\mathrm{2}\right){calculate}\:\:\:{I}\left(\xi\right)\:=\int_{\xi} ^{\mathrm{1}} \:\:\:\:\:\:\frac{{dx}}{\sqrt{\mathrm{1}+\xi{x}^{\mathrm{2}} −\sqrt{\mathrm{1}−\xi{x}^{\mathrm{2}} }}} \\ $$$$\left.\mathrm{1}\right){find}\:{lim}_{\xi\rightarrow\mathrm{0}} \:\:{I}\left(\xi\right) \\ $$

Question Number 84498 Answers: 0 Comments: 1

∫(√x) cos(√x) dx

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

Question Number 84497 Answers: 0 Comments: 1

∫(x^2 /(1+x^5 )) dx

$$\int\frac{{x}^{\mathrm{2}} }{\mathrm{1}+{x}^{\mathrm{5}} }\:{dx} \\ $$$$ \\ $$

Question Number 84467 Answers: 0 Comments: 0

∫ ln(tan^(−1) (x)) dx

$$\int\:\mathrm{ln}\left(\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{x}\right)\right)\:\mathrm{dx} \\ $$

Question Number 84456 Answers: 0 Comments: 1

y=ln(√((a+sin(x))/(b−sin(x)))) if ((dy/dx))^2 −tan^2 (x)=1 show that a=b

$${y}={ln}\sqrt{\frac{{a}+{sin}\left({x}\right)}{{b}−{sin}\left({x}\right)}} \\ $$$${if}\:\left(\frac{{dy}}{{dx}}\right)^{\mathrm{2}} −{tan}^{\mathrm{2}} \left({x}\right)=\mathrm{1} \\ $$$${show}\:{that}\:{a}={b} \\ $$

Question Number 84415 Answers: 3 Comments: 0

∫ (√(x − (√(4 − x^2 )))) dx

$$\int\:\sqrt{\mathrm{x}\:−\:\sqrt{\mathrm{4}\:−\:\mathrm{x}^{\mathrm{2}} }}\:\:\mathrm{dx} \\ $$

Question Number 84399 Answers: 0 Comments: 1

Question Number 84396 Answers: 0 Comments: 2

∫((x(√(x+1)))/(x+2))dx

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

Question Number 84395 Answers: 0 Comments: 0

((x(√(x+1)))/(x+2))

$$\frac{\mathrm{x}\sqrt{\mathrm{x}+\mathrm{1}}}{\mathrm{x}+\mathrm{2}} \\ $$

Question Number 84386 Answers: 1 Comments: 0

∫(√(x−(√(4−x^2 )))) dx

$$\int\sqrt{{x}−\sqrt{\mathrm{4}−{x}^{\mathrm{2}} }}\:{dx} \\ $$

Question Number 84379 Answers: 2 Comments: 0

Question Number 84446 Answers: 0 Comments: 0

Question Number 84334 Answers: 1 Comments: 1

∫((1−u)/(−1−2u+u^2 ))du

$$\int\frac{\mathrm{1}−\mathrm{u}}{−\mathrm{1}−\mathrm{2u}+\mathrm{u}^{\mathrm{2}} }\mathrm{du} \\ $$

Question Number 84313 Answers: 1 Comments: 3

∫ (a^(2/5) −x^(2/5) )^(5/2) dx

$$\int\:\:\left({a}^{\mathrm{2}/\mathrm{5}} −{x}^{\mathrm{2}/\mathrm{5}} \right)^{\frac{\mathrm{5}}{\mathrm{2}}} \:{dx} \\ $$

Question Number 84310 Answers: 0 Comments: 0

Question Number 84246 Answers: 1 Comments: 0

∫cos^n mx dx =

$$\int\mathrm{cos}^{{n}} \:{mx}\:\:{dx}\:= \\ $$

Question Number 84234 Answers: 3 Comments: 2

Integrate the following: 1. ∫(√((a+x)/x)) dx 2.∫ (dx/(sin x(3+2 cos x)))

$$\:\:\boldsymbol{\mathrm{Integrate}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{following}}: \\ $$$$\:\:\:\mathrm{1}.\:\int\sqrt{\frac{\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{x}}}}\:\boldsymbol{\mathrm{dx}} \\ $$$$\:\:\:\mathrm{2}.\int\:\:\frac{\boldsymbol{\mathrm{dx}}}{\boldsymbol{\mathrm{sin}}\:\boldsymbol{\mathrm{x}}\left(\mathrm{3}+\mathrm{2}\:\boldsymbol{\mathrm{cos}}\:\boldsymbol{\mathrm{x}}\right)} \\ $$$$\: \\ $$

Question Number 84165 Answers: 1 Comments: 1

∫_0 ^1 ((ln(x+2))/(x^2 −2x+4)) dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{ln}\left({x}+\mathrm{2}\right)}{{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{4}}\:{dx} \\ $$

Question Number 84163 Answers: 2 Comments: 0

∫ sin (50x) sin^(49) (x) dx ?

$$\int\:\mathrm{sin}\:\left(\mathrm{50}{x}\right)\:\mathrm{sin}\:^{\mathrm{49}} \left({x}\right)\:{dx}\:? \\ $$

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