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IntegrationQuestion and Answers: Page 257

Question Number 51421 Answers: 2 Comments: 3

∫ ((tan^(−1) x)/x^2 ) dx

$$\int\:\:\frac{\mathrm{tan}^{−\mathrm{1}} \mathrm{x}}{\mathrm{x}^{\mathrm{2}} }\:\:\mathrm{dx} \\ $$

Question Number 51419 Answers: 1 Comments: 0

∫ ((√x)/(1 + (x)^(1/3) )) dx

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

Question Number 51394 Answers: 1 Comments: 0

∫ (1/(1 + (√(tan x)))) dx

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

Question Number 51353 Answers: 4 Comments: 1

Question Number 51324 Answers: 2 Comments: 0

calculate ∫_0 ^(+∞) (dx/(1+x^(2 ) +x^4 ))

$${calculate}\:\int_{\mathrm{0}} ^{+\infty} \:\:\:\:\:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{2}\:} \:+{x}^{\mathrm{4}} } \\ $$

Question Number 51215 Answers: 1 Comments: 0

∫_0 ^π e^((1+i)x) dx=...

$$\int_{\mathrm{0}} ^{\pi} {e}^{\left(\mathrm{1}+{i}\right){x}} {dx}=... \\ $$

Question Number 51188 Answers: 0 Comments: 0

find ∫ ((cos^2 x)/(cosx +2sinx))dx

$${find}\:\:\int\:\:\:\:\:\frac{{cos}^{\mathrm{2}} {x}}{{cosx}\:+\mathrm{2}{sinx}}{dx} \\ $$

Question Number 51186 Answers: 1 Comments: 1

calculate ∫_0 ^1 (([nx])/(2x+1))dx

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{\left[{nx}\right]}{\mathrm{2}{x}+\mathrm{1}}{dx} \\ $$

Question Number 51122 Answers: 1 Comments: 1

∫ (dx/(tgx−(√(tgx))))=?

$$\int\:\:\:\:\frac{\boldsymbol{\mathrm{dx}}}{\boldsymbol{\mathrm{tgx}}−\sqrt{\boldsymbol{\mathrm{tgx}}}}=? \\ $$

Question Number 52893 Answers: 1 Comments: 0

∫sin x×cos x dx

$$\int\mathrm{sin}\:{x}×\mathrm{cos}\:{x}\:{dx} \\ $$

Question Number 51047 Answers: 0 Comments: 5

Question Number 50811 Answers: 1 Comments: 2

Question Number 50689 Answers: 1 Comments: 0

If c is the line segement from (0, 0, 0) to (1, 2, 3) find ∫ x e^(yz) ds

$$\mathrm{If}\:\:\mathrm{c}\:\mathrm{is}\:\mathrm{the}\:\mathrm{line}\:\mathrm{segement}\:\mathrm{from}\:\:\left(\mathrm{0},\:\mathrm{0},\:\mathrm{0}\right)\:\mathrm{to}\:\left(\mathrm{1},\:\mathrm{2},\:\mathrm{3}\right) \\ $$$$\mathrm{find}\:\:\:\int\:\mathrm{x}\:\mathrm{e}^{\mathrm{yz}} \:\:\mathrm{ds} \\ $$

Question Number 50683 Answers: 0 Comments: 1

find f(λ) =∫_0 ^∞ ((arctan(λx))/(1+λx^2 ))dx with λ>0

$${find}\:{f}\left(\lambda\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{arctan}\left(\lambda{x}\right)}{\mathrm{1}+\lambda{x}^{\mathrm{2}} }{dx}\:\:{with}\:\lambda>\mathrm{0} \\ $$

Question Number 50659 Answers: 2 Comments: 4

∫_(0 ) ^( ∞) (dx/(4−x^2 )) = ?

$$\int_{\mathrm{0}\:} ^{\:\infty} \:\frac{{dx}}{\mathrm{4}−{x}^{\mathrm{2}} }\:=\:? \\ $$

Question Number 50633 Answers: 1 Comments: 1

please help integrate ((x+sin x)/(1+cos x))dx

$${please}\:{help}\:{integrate}\:\frac{{x}+\mathrm{sin}\:{x}}{\mathrm{1}+\mathrm{cos}\:{x}}{dx} \\ $$

Question Number 50433 Answers: 0 Comments: 0

find all function f C^2 onR / f(x)+∫_0 ^x (x−t)f(t)dt =1 ∀ x∈R .

$${find}\:{all}\:{function}\:{f}\:\:{C}^{\mathrm{2}} \:{onR}\:/ \\ $$$${f}\left({x}\right)+\int_{\mathrm{0}} ^{{x}} \left({x}−{t}\right){f}\left({t}\right){dt}\:=\mathrm{1}\:\forall\:{x}\in{R}\:. \\ $$

Question Number 50427 Answers: 0 Comments: 2

let I_n (λ) =∫_0 ^π ((vos(nt))/(1−2λcost +λ^2 ))dt 1)calculate I_0 (λ) and I_1 (λ) 2) find relation between I_(n−1) ,I_n and I_(n+1) 3) calculate I_n (λ).

$${let}\:{I}_{{n}} \left(\lambda\right)\:=\int_{\mathrm{0}} ^{\pi} \:\:\frac{{vos}\left({nt}\right)}{\mathrm{1}−\mathrm{2}\lambda{cost}\:+\lambda^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{1}\right){calculate}\:{I}_{\mathrm{0}} \left(\lambda\right)\:{and}\:{I}_{\mathrm{1}} \left(\lambda\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{relation}\:{between}\:{I}_{{n}−\mathrm{1}} ,{I}_{{n}} \:{and}\:{I}_{{n}+\mathrm{1}} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:{I}_{{n}} \left(\lambda\right). \\ $$

Question Number 50425 Answers: 0 Comments: 0

find ∫_0 ^∞ ((sin^4 (t))/t^3 ) dt

$${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{sin}^{\mathrm{4}} \left({t}\right)}{{t}^{\mathrm{3}} }\:{dt} \\ $$

Question Number 50422 Answers: 1 Comments: 1

find ∫_0 ^1 ((ln(x))/((√x)(1−x)^(3/2) ))dx

$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{ln}\left({x}\right)}{\sqrt{{x}}\left(\mathrm{1}−{x}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} }{dx} \\ $$

Question Number 50421 Answers: 0 Comments: 1

calculate A =∫_0 ^(π/3) (du/((1+cos^2 u)^3 ))

$${calculate}\:{A}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{3}}} \:\:\:\:\frac{{du}}{\left(\mathrm{1}+{cos}^{\mathrm{2}} {u}\right)^{\mathrm{3}} } \\ $$

Question Number 50420 Answers: 1 Comments: 4

find ∫_0 ^(π/6) cosx ln(cosx)dx

$${find}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{6}}} \:\:{cosx}\:{ln}\left({cosx}\right){dx} \\ $$

Question Number 50418 Answers: 0 Comments: 1

calculate ∫_0 ^(lln(3)) ((sh^2 (x)dx)/(ch^3 (x)))

$${calculate}\:\int_{\mathrm{0}} ^{{lln}\left(\mathrm{3}\right)} \:\:\frac{{sh}^{\mathrm{2}} \left({x}\right){dx}}{{ch}^{\mathrm{3}} \left({x}\right)} \\ $$

Question Number 50417 Answers: 0 Comments: 1

find ∫_0 ^1 arctan(√(1−(x^2 /2)))dx

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

Question Number 50416 Answers: 1 Comments: 0

calculate ∫_0 ^1 ^3 (√(x^2 (1−x^3 )))dx

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:^{\mathrm{3}} \sqrt{{x}^{\mathrm{2}} \left(\mathrm{1}−{x}^{\mathrm{3}} \right)}{dx} \\ $$

Question Number 50415 Answers: 1 Comments: 1

calculate ∫_0 ^(π/2) (dt/(1+cosθ cost))

$${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{dt}}{\mathrm{1}+{cos}\theta\:{cost}} \\ $$

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