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Question Number 84579 Answers: 0 Comments: 0

find ∫ (x^2 −2)(√(x+(1/x)))dx

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

Question Number 84578 Answers: 0 Comments: 4

calculate ∫_0 ^(π/4) (dx/((cosx +3sinx)^2 ))

$${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{dx}}{\left({cosx}\:+\mathrm{3}{sinx}\right)^{\mathrm{2}} } \\ $$

Question Number 84577 Answers: 0 Comments: 2

calculate ∫ (dx/(cosx +cos(2x)+cos(3x)))

$${calculate}\:\int\:\:\:\:\frac{{dx}}{{cosx}\:+{cos}\left(\mathrm{2}{x}\right)+{cos}\left(\mathrm{3}{x}\right)} \\ $$

Question Number 84576 Answers: 0 Comments: 0

find locus of ∣z−(1/z)∣=2∣z^− ∣

$${find}\:{locus}\:{of}\:\:\:\mid{z}−\frac{\mathrm{1}}{{z}}\mid=\mathrm{2}\mid\overset{−} {{z}}\mid \\ $$

Question Number 84575 Answers: 0 Comments: 0

find nature of the serie Σ_(n=1) ^∞ Γ((1/n)) Γ(x)=∫_0 ^∞ t^(x−1) e^(−t) dt (x>0)

$${find}\:{nature}\:{of}\:{the}\:{serie}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\Gamma\left(\frac{\mathrm{1}}{{n}}\right) \\ $$$$\Gamma\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:{t}^{{x}−\mathrm{1}} \:{e}^{−{t}} \:{dt}\:\:\:\:\:\left({x}>\mathrm{0}\right) \\ $$

Question Number 84574 Answers: 0 Comments: 1

calculate I_n =∫_0 ^1 sin(narcsinx)dx

$${calculate}\:\:{I}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:{sin}\left({narcsinx}\right){dx} \\ $$

Question Number 84572 Answers: 0 Comments: 0

let F(z) =(z^2 /(1+z^7 )) 1) factorize inside C[x] and R[x] z^7 +1 2) decompose inside C(x)and R(x) the fraction F(x)

$${let}\:\:{F}\left({z}\right)\:=\frac{{z}^{\mathrm{2}} }{\mathrm{1}+{z}^{\mathrm{7}} } \\ $$$$\left.\mathrm{1}\right)\:{factorize}\:{inside}\:{C}\left[{x}\right]\:{and}\:{R}\left[{x}\right] \\ $$$${z}^{\mathrm{7}} \:+\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{decompose}\:{inside}\:{C}\left({x}\right){and}\:{R}\left({x}\right) \\ $$$${the}\:{fraction}\:{F}\left({x}\right) \\ $$

Question Number 84571 Answers: 0 Comments: 0

calculate S_n =Σ_(k=1) ^n (((−1)^k )/(√k))

$${calculate}\:{S}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\left(−\mathrm{1}\right)^{{k}} }{\sqrt{{k}}} \\ $$

Question Number 84570 Answers: 1 Comments: 1

calculate ∫_1 ^(+∞) ((arctan((3/x)))/x^2 )dx

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

Question Number 84569 Answers: 1 Comments: 0

find ∫ (dx/(1+tan^4 x))

$${find}\:\:\int\:\:\:\:\frac{{dx}}{\mathrm{1}+{tan}^{\mathrm{4}} {x}} \\ $$

Question Number 84568 Answers: 0 Comments: 4

without L′hopital lim_(x→−(1/2)) ((2x^3 +3x^2 −(√(a+bx)))/(4x^2 −1)) = −(3/4) find a+b

$$\mathrm{without}\:\mathrm{L}'\mathrm{hopital} \\ $$$$\underset{{x}\rightarrow−\frac{\mathrm{1}}{\mathrm{2}}} {\mathrm{lim}}\:\frac{\mathrm{2x}^{\mathrm{3}} +\mathrm{3x}^{\mathrm{2}} −\sqrt{\mathrm{a}+\mathrm{bx}}}{\mathrm{4x}^{\mathrm{2}} −\mathrm{1}}\:=\:−\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\mathrm{find}\:\mathrm{a}+\mathrm{b} \\ $$

Question Number 84566 Answers: 0 Comments: 0

Question Number 84564 Answers: 0 Comments: 1

find arg(z) given that z = ((1 + i)/(1−i))

$$\mathrm{find}\:\mathrm{arg}\left(\mathrm{z}\right)\:\mathrm{given}\:\mathrm{that}\:\:\mathrm{z}\:=\:\frac{\mathrm{1}\:+\:{i}}{\mathrm{1}−{i}} \\ $$

Question Number 84561 Answers: 1 Comments: 0

∫_0 ^∞ ∫_0 ^∞ ((cos(x−y)−cos(x))/(xy))dx dy

$$\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\infty} \frac{{cos}\left({x}−{y}\right)−{cos}\left({x}\right)}{{xy}}{dx}\:{dy} \\ $$

Question Number 84558 Answers: 0 Comments: 1

happy π day

$${happy}\:\pi\:{day} \\ $$

Question Number 84557 Answers: 0 Comments: 1

Question Number 84556 Answers: 1 Comments: 1

∫ sin^(−1) (((2x+2)/(√(4x^2 +8x+13)))) dx

$$\int\:\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{2x}+\mathrm{2}}{\sqrt{\mathrm{4x}^{\mathrm{2}} +\mathrm{8x}+\mathrm{13}}}\right)\:\mathrm{dx} \\ $$

Question Number 84553 Answers: 0 Comments: 3

Find mininum value of n such that both n + 3 and 2020n + 1 are square numbers .

$${Find}\:\:{mininum}\:\:{value}\:\:{of}\:\:{n}\:\:{such}\:\:{that} \\ $$$${both}\:\:{n}\:+\:\mathrm{3}\:\:\:{and}\:\:\mathrm{2020}{n}\:+\:\mathrm{1}\:\:{are}\:\:{square}\:\:{numbers}\:. \\ $$

Question Number 84549 Answers: 1 Comments: 0

Question Number 84544 Answers: 0 Comments: 0

solve xy^(′′) =y^′ (e^y −1)

$${solve}\: \\ $$$${xy}^{''} ={y}^{'} \left({e}^{{y}} −\mathrm{1}\right) \\ $$

Question Number 84543 Answers: 0 Comments: 3

Determine the value of a,b ,c so that _(x→0) ^(lim) (((a +b cos x) x−c sin x)/x^5 )=1

Question Number 84532 Answers: 1 Comments: 1

x> 0 , y > 0 prove that ((xy)/(x+y)) < x

$$\mathrm{x}>\:\mathrm{0}\:,\:\mathrm{y}\:>\:\mathrm{0}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{xy}}{\mathrm{x}+\mathrm{y}}\:<\:\mathrm{x} \\ $$

Question Number 84531 Answers: 1 Comments: 2

find for equation of image ellipse (x^2 /9) + (y^2 /8) = 1 if reflected with line x + y = −4

$$\mathrm{find}\:\mathrm{for}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{image}\:\mathrm{ellipse} \\ $$$$\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{9}}\:+\:\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{8}}\:=\:\mathrm{1}\:\mathrm{if}\:\mathrm{reflected}\:\mathrm{with}\:\mathrm{line} \\ $$$$\mathrm{x}\:+\:\mathrm{y}\:=\:−\mathrm{4} \\ $$

Question Number 84528 Answers: 0 Comments: 3

1=2

$$\mathrm{1}=\mathrm{2} \\ $$

Question Number 84515 Answers: 1 Comments: 0

Q.solve x^3 −x=x!

$${Q}.{solve} \\ $$$${x}^{\mathrm{3}} −{x}={x}! \\ $$

Question Number 84512 Answers: 1 Comments: 0

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