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Question Number 46856    Answers: 0   Comments: 1

find f(t) =∫_0 ^1 x^2 arctan(1+tx)dx

$${find}\:{f}\left({t}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}^{\mathrm{2}} \:{arctan}\left(\mathrm{1}+{tx}\right){dx}\: \\ $$

Question Number 46855    Answers: 0   Comments: 1

calculate ∫_0 ^1 x arctan(1+x)dx

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

Question Number 46854    Answers: 1   Comments: 1

find =∫_0 ^π ((sinx)/(2+cos(2x)))dx

$${find}\:\:=\int_{\mathrm{0}} ^{\pi} \:\:\:\frac{{sinx}}{\mathrm{2}+{cos}\left(\mathrm{2}{x}\right)}{dx} \\ $$

Question Number 46853    Answers: 1   Comments: 1

fnd ∫ (dx/(1+cos(tx)))

$${fnd}\:\:\int\:\:\:\:\:\:\frac{{dx}}{\mathrm{1}+{cos}\left({tx}\right)} \\ $$

Question Number 46852    Answers: 1   Comments: 1

find the value of Σ_(n=1) ^∞ (n^3 /3^n )

$${find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{{n}^{\mathrm{3}} }{\mathrm{3}^{{n}} } \\ $$

Question Number 46851    Answers: 0   Comments: 3

let f(x)=∫_0 ^(2π) ((sint)/(x +sint))dt withx>1 1) calculate f(x) 2) calculate ∫_0 ^(2π) ((sint)/((x+sint)^2 ))dt 3)find the value of ∫_0 ^(2π) ((sint)/(2+sint))dt and ∫_0 ^(2π) ((sint)/((2+sint)^2 ))dt

$${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{sint}}{{x}\:+{sint}}{dt}\:\:{withx}>\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{sint}}{\left({x}+{sint}\right)^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{3}\right){find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{sint}}{\mathrm{2}+{sint}}{dt}\:{and}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{sint}}{\left(\mathrm{2}+{sint}\right)^{\mathrm{2}} }{dt} \\ $$

Question Number 46850    Answers: 1   Comments: 1

let a^2 >b^(2 ) +c^2 calculate ∫_0 ^(2π) (dθ/(a+bsinθ +c cosθ))

$${let}\:{a}^{\mathrm{2}} >{b}^{\mathrm{2}\:} +{c}^{\mathrm{2}} \:\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{d}\theta}{{a}+{bsin}\theta\:+{c}\:{cos}\theta} \\ $$

Question Number 46849    Answers: 0   Comments: 0

let A_p =Σ_(n=1) ^∞ n^p x^n with p integr . and x ∈]−1,1[ . 1) calculate A_1 ,A_2 and A_3 2) find a relation of recurrence betwen the A_n 3) calculate Σ_(n=1) ^∞ n^4 x^n and Σ_(n=1) ^∞ n^5 x^n .

$$\left.{let}\:{A}_{{p}} =\sum_{{n}=\mathrm{1}} ^{\infty} \:{n}^{{p}} {x}^{{n}} \:\:\:\:{with}\:{p}\:{integr}\:.\:{and}\:{x}\:\in\right]−\mathrm{1},\mathrm{1}\left[\:.\right. \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{\mathrm{1}} ,{A}_{\mathrm{2}} \:{and}\:{A}_{\mathrm{3}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{a}\:{relation}\:{of}\:{recurrence}\:\:{betwen}\:{the}\:{A}_{{n}} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:{n}^{\mathrm{4}} {x}^{{n}} \:{and}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:{n}^{\mathrm{5}} {x}^{{n}} \:. \\ $$

Question Number 46848    Answers: 0   Comments: 1

caculate ∫∫_D (x^2 −y^2 ) e^(−x^2 −y^2 ) dxdy with D ={(x,y)∈R^2 / x^2 +y^2 ≤4}

$${caculate}\:\:\int\int_{{D}} \:\:\left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right)\:{e}^{−{x}^{\mathrm{2}} \:−{y}^{\mathrm{2}} } {dxdy}\:\:{with} \\ $$$${D}\:=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:\:\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:\leqslant\mathrm{4}\right\} \\ $$

Question Number 46847    Answers: 0   Comments: 1

calculate ∫∫_(0≤x≤1 and 1≤y≤2) e^(x/y) dxdy

$${calculate}\:\:\int\int_{\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:{and}\:\mathrm{1}\leqslant{y}\leqslant\mathrm{2}} \:\:{e}^{\frac{{x}}{{y}}} {dxdy} \\ $$

Question Number 46846    Answers: 0   Comments: 1

calculate ∫∫_D ((x+y)/(√(1−x^2 −y^2 )))dxdy with D={(x,y)∈R^2 /x≥0,y≥0,x^2 +y^2 <1}

$${calculate}\:\int\int_{{D}} \:\:\:\:\frac{{x}+{y}}{\sqrt{\mathrm{1}−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} }}{dxdy}\:{with}\:{D}=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /{x}\geqslant\mathrm{0},{y}\geqslant\mathrm{0},{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} <\mathrm{1}\right\} \\ $$

Question Number 46845    Answers: 0   Comments: 0

calculate ∫_0 ^1 (e^(−x) /(1+x)) dx .

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{e}^{−{x}} }{\mathrm{1}+{x}}\:{dx}\:. \\ $$

Question Number 46844    Answers: 0   Comments: 1

calculate ∫_0 ^∞ e^(−2t) ln(1+3t)dt

$${calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−\mathrm{2}{t}} {ln}\left(\mathrm{1}+\mathrm{3}{t}\right){dt}\: \\ $$

Question Number 46843    Answers: 0   Comments: 0

let f(x)= ∫_0 ^x (t/(sin(t)))dt 1) find a explicit form of f(x) 2) calculate ∫_0 ^(π/2) (t/(sint))dt

$${let}\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{{x}} \:\frac{{t}}{{sin}\left({t}\right)}{dt} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{t}}{{sint}}{dt} \\ $$

Question Number 46842    Answers: 1   Comments: 1

find ∫ (dx/(x(√(x−x^2 ))))

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

Question Number 46841    Answers: 1   Comments: 1

calculate ∫_(π/4) ^(π/3) (dx/(cosx sinx))

$${calculate}\:\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{3}}} \:\:\:\frac{{dx}}{{cosx}\:{sinx}} \\ $$

Question Number 46840    Answers: 0   Comments: 1

find lim_(n→+∞) Σ_(k=1) ^n ((n^(2 ) +k^2 )/(n^3 +k^3 ))

$${find}\:{lim}_{{n}\rightarrow+\infty} \:\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{{n}^{\mathrm{2}\:} +{k}^{\mathrm{2}} }{{n}^{\mathrm{3}} \:+{k}^{\mathrm{3}} } \\ $$

Question Number 46838    Answers: 1   Comments: 0

Question Number 46837    Answers: 0   Comments: 1

find∫(√(sin2x)) dx=??

$${find}\int\sqrt{{sin}\mathrm{2}{x}}\:{dx}=?? \\ $$

Question Number 46833    Answers: 0   Comments: 1

Question Number 46831    Answers: 0   Comments: 0

Question Number 46829    Answers: 1   Comments: 0

Question Number 46827    Answers: 0   Comments: 0

Question Number 46821    Answers: 1   Comments: 0

Question Number 46816    Answers: 1   Comments: 0

Question Number 46814    Answers: 1   Comments: 0

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