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Question Number 39020    Answers: 1   Comments: 0

calculate ∫_0 ^1 ((ln(1+(√(x^2 +1))))/(√(x^2 +1))) dx

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

Question Number 39019    Answers: 1   Comments: 3

calculate ∫ (dx/((x^2 +1)(x^2 +2)(x^2 +3))) 1) find the value of ∫_0 ^∞ (dx/((x^2 +1)(x^2 +2)(x^2 +3)))

$${calculate}\:\int\:\:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{2}\right)\left({x}^{\mathrm{2}} \:+\mathrm{3}\right)} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)\left({x}^{\mathrm{2}} \:+\mathrm{2}\right)\left({x}^{\mathrm{2}} \:+\mathrm{3}\right)} \\ $$

Question Number 39017    Answers: 0   Comments: 1

find ∫ ((−2x+3)/(x^2 ( x^3 +8)))dx 2) calculate ∫_1 ^(+∞) ((−2x+3)/(x^2 (x^3 +8)))dx

$${find}\:\:\:\int\:\:\frac{−\mathrm{2}{x}+\mathrm{3}}{{x}^{\mathrm{2}} \left(\:{x}^{\mathrm{3}} \:+\mathrm{8}\right)}{dx} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{1}} ^{+\infty} \:\:\:\frac{−\mathrm{2}{x}+\mathrm{3}}{{x}^{\mathrm{2}} \left({x}^{\mathrm{3}} \:+\mathrm{8}\right)}{dx} \\ $$

Question Number 39016    Answers: 0   Comments: 0

calculate ∫_0 ^π ((sin(nx))/(cosx))dx with n from N .

$${calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\frac{{sin}\left({nx}\right)}{{cosx}}{dx}\:\:{with}\:{n}\:{from}\:{N}\:. \\ $$

Question Number 39015    Answers: 0   Comments: 2

find ∫ (dx/(x(2x+1)(3x+2))) 2) calculate ∫_1 ^2 (dx/(x(2x+1)(3x+2)))

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

Question Number 38946    Answers: 0   Comments: 0

find ∫ arcos(2(√(1−x^2 )))dx .

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

Question Number 38899    Answers: 0   Comments: 4

find ∫_0 ^π ln(2+cost)dt and ∫_0 ^π ln(2−cost)dt

$${find}\:\int_{\mathrm{0}} ^{\pi} {ln}\left(\mathrm{2}+{cost}\right){dt}\:{and}\:\int_{\mathrm{0}} ^{\pi} {ln}\left(\mathrm{2}−{cost}\right){dt} \\ $$

Question Number 38897    Answers: 0   Comments: 0

find ∫ ln((√x) +(√(x+1)) +(√(x+2)))dx

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

Question Number 38896    Answers: 1   Comments: 2

let A_n = ∫_0 ^n ((x[x])/(1+x^2 )) dx 1) calculate A_n 2) find lim_(n→+∞) A_n

$${let}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{{n}} \:\:\:\frac{{x}\left[{x}\right]}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$

Question Number 39030    Answers: 2   Comments: 3

1) let f(x) = ∫_0 ^∞ (dt/(1+x^2 t^4 )) with x >0 find a simple form of f(x) 2) calculate ∫_0 ^(+∞) (dt/(1+t^4 )) 3) calculate ∫_0 ^∞ (dt/(1+3t^4 ))

$$\left.\mathrm{1}\right)\:{let}\:{f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dt}}{\mathrm{1}+{x}^{\mathrm{2}} {t}^{\mathrm{4}} }\:\:{with}\:{x}\:>\mathrm{0} \\ $$$${find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{+\infty} \:\:\:\frac{{dt}}{\mathrm{1}+{t}^{\mathrm{4}} } \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dt}}{\mathrm{1}+\mathrm{3}{t}^{\mathrm{4}} } \\ $$

Question Number 38804    Answers: 1   Comments: 3

let A_n = ∫_0 ^n (((−1)^x )/(2[x] +1))dx 1) calculate A_n 2) find lim_(n→+∞) A_n

$${let}\:\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{{n}} \:\:\:\frac{\left(−\mathrm{1}\right)^{{x}} }{\mathrm{2}\left[{x}\right]\:+\mathrm{1}}{dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$

Question Number 39029    Answers: 2   Comments: 0

∫((3−5(√(1−(1/x)))))^(1/3) dx=? ∫(1/((3−5(√(1−(1/x)))))^(1/3) )dx=?

$$\int\sqrt[{\mathrm{3}}]{\mathrm{3}−\mathrm{5}\sqrt{\mathrm{1}−\frac{\mathrm{1}}{{x}}}}{dx}=? \\ $$$$\int\frac{\mathrm{1}}{\sqrt[{\mathrm{3}}]{\mathrm{3}−\mathrm{5}\sqrt{\mathrm{1}−\frac{\mathrm{1}}{{x}}}}}{dx}=? \\ $$

Question Number 38746    Answers: 0   Comments: 3

this is still waiting to be solved... ∫((√((t−1)t(t+1)))/(3t^2 −4))dt=?

$$\mathrm{this}\:\mathrm{is}\:\mathrm{still}\:\mathrm{waiting}\:\mathrm{to}\:\mathrm{be}\:\mathrm{solved}... \\ $$$$\int\frac{\sqrt{\left({t}−\mathrm{1}\right){t}\left({t}+\mathrm{1}\right)}}{\mathrm{3}{t}^{\mathrm{2}} −\mathrm{4}}{dt}=? \\ $$

Question Number 38728    Answers: 0   Comments: 1

find L ( (e^(−(x/a)) /a)) with a≠0 and L laplace transfom.

$${find}\:{L}\:\left(\:\frac{{e}^{−\frac{{x}}{{a}}} }{{a}}\right)\:\:{with}\:{a}\neq\mathrm{0}\:\:{and}\:{L}\:{laplace}\:{transfom}. \\ $$

Question Number 38727    Answers: 0   Comments: 2

let n from N and A_n = ∫_(−∞) ^(+∞) ((cos(ax))/((x^2 +x+1)^n ))dx and B_n = ∫_(−∞) ^(+∞) ((sin(ax))/((x^2 +x+1)^n ))dx find the value of A_(n ) and B_n .

$${let}\:{n}\:{from}\:{N}\:\:{and}\:\:{A}_{{n}} =\:\int_{−\infty} ^{+\infty} \:\:\:\:\frac{{cos}\left({ax}\right)}{\left({x}^{\mathrm{2}} \:+{x}+\mathrm{1}\right)^{{n}} }{dx}\:\:{and} \\ $$$${B}_{{n}} =\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{sin}\left({ax}\right)}{\left({x}^{\mathrm{2}} \:+{x}+\mathrm{1}\right)^{{n}} }{dx} \\ $$$${find}\:{the}\:{value}\:{of}\:{A}_{{n}\:} \:\:{and}\:{B}_{{n}} \:\:. \\ $$$$ \\ $$

Question Number 38724    Answers: 0   Comments: 2

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

$${calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{x}^{\mathrm{2}} {cos}\left(\pi{x}\right)}{\left({x}^{\mathrm{2}} \:+\mathrm{4}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 38718    Answers: 0   Comments: 3

1) find f(x)=∫_0 ^π ln(2+x cosθ)dθ 2) calculate ∫_0 ^π ln(2 +cosθ)dθ

$$\left.\mathrm{1}\right)\:{find}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\pi} \:{ln}\left(\mathrm{2}+{x}\:{cos}\theta\right){d}\theta \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\pi} \:{ln}\left(\mathrm{2}\:\:+{cos}\theta\right){d}\theta \\ $$$$ \\ $$

Question Number 38720    Answers: 0   Comments: 2

find ∫ (((√(x+1)) −(√(x−1)))/((√(x+1)) −(√(x−1))))dx

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

Question Number 38719    Answers: 1   Comments: 0

find ∫ ln((√x) +(√(x+1)))dx

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

Question Number 38716    Answers: 1   Comments: 1

calculate ∫_2 ^5 (dx/((x +1−[x])^2 ))

$${calculate}\:\:\:\int_{\mathrm{2}} ^{\mathrm{5}} \:\:\:\:\:\frac{{dx}}{\left({x}\:+\mathrm{1}−\left[{x}\right]\right)^{\mathrm{2}} } \\ $$

Question Number 38714    Answers: 1   Comments: 1

calculate ∫_1 ^6 (((−1)^([x]) )/(1+x^2 [x]))dx

$${calculate}\:\:\:\int_{\mathrm{1}} ^{\mathrm{6}} \:\:\:\:\frac{\left(−\mathrm{1}\right)^{\left[{x}\right]} }{\mathrm{1}+{x}^{\mathrm{2}} \left[{x}\right]}{dx} \\ $$

Question Number 38706    Answers: 0   Comments: 4

let f(x)= ∫_0 ^(π/2) (dθ/(1+x e^(iθ) )) with ∣x∣<1 1) developp f(x) at integr serie 2) calculate f(x) 3) find the value of ∫_0 ^(π/2) (e^(iθ) /((1+x e^(iθ) )^2 )) 4) calculate ∫_0 ^(π/2) (dθ/(2 +e^(iθ) ))

$${let}\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\frac{{d}\theta}{\mathrm{1}+{x}\:{e}^{{i}\theta} }\:\:\:\:\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{developp}\:{f}\left({x}\right)\:{at}\:{integr}\:{serie} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{e}^{{i}\theta} }{\left(\mathrm{1}+{x}\:{e}^{{i}\theta} \right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\:\frac{{d}\theta}{\mathrm{2}\:+{e}^{{i}\theta} } \\ $$

Question Number 38651    Answers: 1   Comments: 0

If ∫_0 ^1 e^(−x^2 ) dx = a , then find the value of ∫_0 ^1 x^2 e^(−x^2 ) dx in terms of ′a′ ?

$$\mathrm{If}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\mathrm{e}^{−{x}^{\mathrm{2}} } {dx}\:=\:{a}\:,\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{\mathrm{2}} {e}^{−{x}^{\mathrm{2}} } {dx}\:{in}\:{terms}\:{of}\:'{a}'\:? \\ $$

Question Number 38536    Answers: 2   Comments: 0

∫_0 ^π (dx/(√(3−cos x)))=

$$\int_{\mathrm{0}} ^{\pi} \frac{{dx}}{\sqrt{\mathrm{3}−\mathrm{cos}\:{x}}}= \\ $$

Question Number 38516    Answers: 3   Comments: 1

∫_0 ^(π/2) ∣sin x − cos x∣dx

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\mid\mathrm{sin}\:{x}\:−\:\mathrm{cos}\:{x}\mid\mathrm{d}{x} \\ $$

Question Number 38470    Answers: 0   Comments: 4

calculate f(t)=∫_0 ^∞ ((cos(tx))/((1+tx^2 )^2 )) dx with t≥0 2) find the values of ∫_0 ^∞ ((cos(2x))/((1+2x^2 )^2 ))dx and ∫_0 ^∞ ((cosx)/((2+x^2 )^2 ))dx

$${calculate}\:{f}\left({t}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({tx}\right)}{\left(\mathrm{1}+{tx}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{dx}\:{with}\:{t}\geqslant\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{values}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left(\mathrm{2}{x}\right)}{\left(\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx}\:\:{and}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{cosx}}{\left(\mathrm{2}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx} \\ $$

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