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IntegrationQuestion and Answers: Page 223

Question Number 67385 Answers: 0 Comments: 0

find ∫ x((√((1−x^2 )/(1+x^2 ))))dx

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

Question Number 67374 Answers: 0 Comments: 3

find ∫ (1+(1/x^2 ))arctan(1−(1/x))dx

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

Question Number 67373 Answers: 1 Comments: 4

simplify S_n (x) =Σ_(k=0) ^n C_n ^k cos^4 (πkx) 2) calculate I_n =∫_0 ^(1/3) S_n (x)dx

$${simplify}\:\:\:{S}_{{n}} \left({x}\right)\:=\sum_{{k}=\mathrm{0}} ^{{n}} \:{C}_{{n}} ^{{k}} \:{cos}^{\mathrm{4}} \left(\pi{kx}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{I}_{{n}} =\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{3}}} \:{S}_{{n}} \left({x}\right){dx} \\ $$

Question Number 67359 Answers: 1 Comments: 1

∫siny/y dy

$$\int{siny}/{y}\:\:{dy} \\ $$

Question Number 67342 Answers: 0 Comments: 1

find the value of ∫_(−∞) ^∞ ((sin(2x^2 ))/((x^2 −x +3)^3 ))dx

$${find}\:{the}\:{value}\:{of}\:\int_{−\infty} ^{\infty} \:\:\:\frac{{sin}\left(\mathrm{2}{x}^{\mathrm{2}} \right)}{\left({x}^{\mathrm{2}} −{x}\:+\mathrm{3}\right)^{\mathrm{3}} }{dx} \\ $$

Question Number 67310 Answers: 1 Comments: 2

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

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

Question Number 67246 Answers: 2 Comments: 4

Integrate: 1) ∫_3 ^( ∞) ((1/x dx)/(ln(x)(√(ln^2 x−1)))) 2) ∫_1 ^∞ ((e^x dx)/(1+e^(2x) )) 3) ∫_1 ^∞ ((2^x dx)/(x+1)) 4) ∫_2 ^∞ ((√x)/(ln(x)))dx

$${Integrate}: \\ $$$$\left.\mathrm{1}\right)\:\underset{\mathrm{3}} {\overset{\:\infty} {\int}}\:\frac{\mathrm{1}/{x}\:{dx}}{{ln}\left({x}\right)\sqrt{{ln}^{\mathrm{2}} {x}−\mathrm{1}}} \\ $$$$\left.\mathrm{2}\right)\:\underset{\mathrm{1}} {\overset{\infty} {\int}}\frac{{e}^{{x}} {dx}}{\mathrm{1}+{e}^{\mathrm{2}{x}} } \\ $$$$\left.\mathrm{3}\right)\:\underset{\mathrm{1}} {\overset{\infty} {\int}}\:\frac{\mathrm{2}^{{x}} {dx}}{{x}+\mathrm{1}} \\ $$$$\left.\mathrm{4}\right)\:\underset{\mathrm{2}} {\overset{\infty} {\int}}\:\frac{\sqrt{{x}}}{{ln}\left({x}\right)}{dx} \\ $$

Question Number 67235 Answers: 0 Comments: 1

find ∫_(−(π/3)) ^(π/3) x^2 {cosx−sinx}^3 dx

$${find}\:\:\int_{−\frac{\pi}{\mathrm{3}}} ^{\frac{\pi}{\mathrm{3}}} \:{x}^{\mathrm{2}} \left\{{cosx}−{sinx}\right\}^{\mathrm{3}} {dx} \\ $$

Question Number 67233 Answers: 0 Comments: 1

calculate ∫_0 ^1 ((xdx)/(√(1+x^4 )))

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{xdx}}{\sqrt{\mathrm{1}+{x}^{\mathrm{4}} }} \\ $$

Question Number 67231 Answers: 2 Comments: 0

find ∫x/x^5 −1) dx

$$\left.{find}\:\int{x}/{x}^{\mathrm{5}} −\mathrm{1}\right)\:{dx} \\ $$

Question Number 67197 Answers: 1 Comments: 0

∫_0 ^2 x^5 (1−(x/2))^4 dx

$$\int_{\mathrm{0}} ^{\mathrm{2}} {x}^{\mathrm{5}} \left(\mathrm{1}−\frac{{x}}{\mathrm{2}}\right)^{\mathrm{4}} {dx} \\ $$

Question Number 67153 Answers: 2 Comments: 0

find ∫(v^3 −2)/(v^4 +v )dv

$${find}\:\int\left({v}^{\mathrm{3}} −\mathrm{2}\right)/\left({v}^{\mathrm{4}} +{v}\:\:\right){dv} \\ $$

Question Number 67138 Answers: 0 Comments: 1

find the area abounded y=(√x) and y=x−2?

$${find}\:{the}\:{area}\:{abounded}\:{y}=\sqrt{{x}} \\ $$$${and}\:{y}={x}−\mathrm{2}? \\ $$

Question Number 67106 Answers: 0 Comments: 1

find the area abounded y=(√x) afind y=x−2?

$${find}\:{the}\:{area}\:{abounded}\:{y}=\sqrt{{x}} \\ $$$${afind}\:{y}={x}−\mathrm{2}? \\ $$

Question Number 67105 Answers: 0 Comments: 0

find the area abounded y=(√x) afind y=x−2?

$${find}\:{the}\:{area}\:{abounded}\:{y}=\sqrt{{x}} \\ $$$${afind}\:{y}={x}−\mathrm{2}? \\ $$

Question Number 67070 Answers: 0 Comments: 3

Question Number 67069 Answers: 0 Comments: 1

Question Number 67059 Answers: 0 Comments: 1

find the area abounded y=(√(x−2)) and y=x−2 ?

$${find}\:{the}\:{area}\:{abounded}\:{y}=\sqrt{{x}−\mathrm{2}} \\ $$$${and}\:{y}={x}−\mathrm{2}\:? \\ $$

Question Number 67058 Answers: 0 Comments: 0

find the area abounded y=(√(x−2)) and y=x−2 ?

$${find}\:{the}\:{area}\:{abounded}\:{y}=\sqrt{{x}−\mathrm{2}} \\ $$$${and}\:{y}={x}−\mathrm{2}\:? \\ $$

Question Number 67038 Answers: 1 Comments: 1

calculate ∫_(−1) ^1 (x^(2n) /(1+2^(sinx) ))dx with n integr.

$${calculate}\:\:\int_{−\mathrm{1}} ^{\mathrm{1}} \:\frac{{x}^{\mathrm{2}{n}} }{\mathrm{1}+\mathrm{2}^{{sinx}} }{dx}\:\:\:{with}\:{n}\:{integr}. \\ $$

Question Number 67035 Answers: 1 Comments: 2

Question Number 67022 Answers: 0 Comments: 0

find ∫ (1+(√x))(√(x^2 +3))dx

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

Question Number 67021 Answers: 0 Comments: 1

find f(x) =∫_0 ^1 ln(x +e^(−t) )dt with x>0

$${find}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left({x}\:+{e}^{−{t}} \right){dt}\:\:\:{with}\:{x}>\mathrm{0} \\ $$

Question Number 67020 Answers: 0 Comments: 1

find f(x) = ∫_0 ^1 arctan(1+xt)dt with x real

$${find}\:{f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{arctan}\left(\mathrm{1}+{xt}\right){dt}\:\:{with}\:{x}\:{real} \\ $$

Question Number 67019 Answers: 0 Comments: 0

calculate ∫_0 ^∞ e^(−x^2 ) arctan(x^2 )dx

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

Question Number 67018 Answers: 0 Comments: 1

find ∫_0 ^∞ e^(−x) ln(1+x)dx

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

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