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Question Number 46906 Answers: 0 Comments: 1

Question Number 46898 Answers: 2 Comments: 2

∫((tanx)/((tanx+1)^2 −2tan^2 x ))dx=??

$$\int\frac{{tanx}}{\left({tanx}+\mathrm{1}\right)^{\mathrm{2}} −\mathrm{2}{tan}^{\mathrm{2}} {x}\:\:}{dx}=?? \\ $$

Question Number 46891 Answers: 1 Comments: 0

X can finish a work in 15 days at 8hrs. a day. Y can finish it in 6(2/3) days at 9 hrs. a day. Find in how many days X and Y can finish it working together 10 hrs. a day?

$$\mathrm{X}\:\mathrm{can}\:\mathrm{finish}\:\mathrm{a}\:\mathrm{work}\:\mathrm{in}\:\mathrm{15}\:\mathrm{days}\:\mathrm{at}\:\mathrm{8hrs}. \\ $$$$\mathrm{a}\:\mathrm{day}.\:\mathrm{Y}\:\mathrm{can}\:\mathrm{finish}\:\mathrm{it}\:\mathrm{in}\:\mathrm{6}\frac{\mathrm{2}}{\mathrm{3}}\:\mathrm{days}\:\mathrm{at} \\ $$$$\mathrm{9}\:\mathrm{hrs}.\:\mathrm{a}\:\mathrm{day}.\:\mathrm{Find}\:\mathrm{in}\:\mathrm{how}\:\mathrm{many}\:\mathrm{days} \\ $$$$\mathrm{X}\:\mathrm{and}\:\mathrm{Y}\:\mathrm{can}\:\mathrm{finish}\:\mathrm{it}\:\mathrm{working}\:\mathrm{together}\: \\ $$$$\mathrm{10}\:\mathrm{hrs}.\:\mathrm{a}\:\mathrm{day}? \\ $$

Question Number 46889 Answers: 1 Comments: 1

Question Number 46882 Answers: 0 Comments: 2

factorize inside C[x] x^2 +y^2 +z^2

$${factorize}\:{inside}\:{C}\left[{x}\right]\:\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:+{z}^{\mathrm{2}} \\ $$

Question Number 46881 Answers: 0 Comments: 1

factorize inside C[x] the polynom x^n +y^n

$${factorize}\:{inside}\:{C}\left[{x}\right]\:{the}\:{polynom}\:\:{x}^{{n}} \:+{y}^{{n}} \\ $$

Question Number 46880 Answers: 0 Comments: 0

factorize inside C[x] x^n −y^n with n natural integr

$${factorize}\:{inside}\:{C}\left[{x}\right]\:{x}^{{n}} −{y}^{{n}} \:\:{with}\:{n}\:{natural}\:{integr} \\ $$

Question Number 46864 Answers: 1 Comments: 2

Question Number 46860 Answers: 1 Comments: 2

Find the sum to infinity whose n^(th) term is (n/2^(n−1) ) .

$$\:\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{to}\:\mathrm{infinity}\:\mathrm{whose}\:\mathrm{n}^{\mathrm{th}} \:\mathrm{term}\:\mathrm{is}\:\frac{\mathrm{n}}{\mathrm{2}^{\mathrm{n}−\mathrm{1}} }\:. \\ $$

Question Number 46858 Answers: 0 Comments: 0

solve (1+x^2 )y^(′′) −((2x)/(x^3 +1))y^′ +xy =x e^(−2x) .

$${solve}\:\left(\mathrm{1}+{x}^{\mathrm{2}} \right){y}^{''} \:−\frac{\mathrm{2}{x}}{{x}^{\mathrm{3}} \:+\mathrm{1}}{y}^{'} \:\:+{xy}\:={x}\:{e}^{−\mathrm{2}{x}} . \\ $$

Question Number 46857 Answers: 1 Comments: 2

solve 2x y^′ +(1+x^2 )y =xe^(−x) withy(o)=1

$${solve}\:\mathrm{2}{x}\:{y}^{'} \:+\left(\mathrm{1}+{x}^{\mathrm{2}} \right){y}\:={xe}^{−{x}} \:\:\:{withy}\left({o}\right)=\mathrm{1}\: \\ $$

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 .