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Question Number 88197 Answers: 0 Comments: 0

prove that ∫_0 ^1 (√(((x^2 −2)/(x^2 −1)) ))dx=((π(√(2π)))/(Γ^2 ((1/4))))+((Γ^2 ((1/4)))/(4(√(2π))))

$${prove}\:{that}\: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\frac{{x}^{\mathrm{2}} −\mathrm{2}}{{x}^{\mathrm{2}} −\mathrm{1}}\:}{dx}=\frac{\pi\sqrt{\mathrm{2}\pi}}{\Gamma^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{4}}\right)}+\frac{\Gamma^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{4}}\right)}{\mathrm{4}\sqrt{\mathrm{2}\pi}} \\ $$

Question Number 88196 Answers: 0 Comments: 0

Question Number 88194 Answers: 0 Comments: 4

find ∫(1/((√x)+(√(x+1))+(√(x+2)))) dx

$${find}\:\int\frac{\mathrm{1}}{\sqrt{{x}}+\sqrt{{x}+\mathrm{1}}+\sqrt{{x}+\mathrm{2}}}\:{dx} \\ $$$$ \\ $$

Question Number 88188 Answers: 1 Comments: 5

Question Number 88181 Answers: 0 Comments: 1

Question Number 88180 Answers: 0 Comments: 0

(5+4y)×dy=y^3 x

$$\left(\mathrm{5}+\mathrm{4}{y}\right)×{dy}={y}^{\mathrm{3}} {x}\: \\ $$

Question Number 88179 Answers: 1 Comments: 0

z=x^2 /y^3 dz=?

$${z}={x}^{\mathrm{2}} /{y}^{\mathrm{3}} \:\:\:\:\:\:\:\:\:\:{dz}=? \\ $$

Question Number 88178 Answers: 0 Comments: 0

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Question Number 88177 Answers: 1 Comments: 0

prove that ∫_0 ^(2020) (x−[x])(√(x−[x])) dx=808

$${prove}\:{that} \\ $$$$ \\ $$$$\int_{\mathrm{0}} ^{\mathrm{2020}} \left({x}−\left[{x}\right]\right)\sqrt{{x}−\left[{x}\right]}\:{dx}=\mathrm{808} \\ $$

Question Number 88170 Answers: 0 Comments: 2

Prove that ∫_0 ^1 tcos nπtdt=(((−1)^n −1)/(n^2 π^2 ))

$${Prove}\:{that}\: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} {tcos}\:{n}\pi{tdt}=\frac{\left(−\mathrm{1}\right)^{{n}} −\mathrm{1}}{{n}^{\mathrm{2}} \pi^{\mathrm{2}} } \\ $$

Question Number 88169 Answers: 1 Comments: 2

find Laplace transform t^3 . cos 4t

$$\mathrm{find}\:\mathrm{Laplace}\:\mathrm{transform}\: \\ $$$$\mathrm{t}^{\mathrm{3}} .\:\mathrm{cos}\:\:\mathrm{4t} \\ $$

Question Number 88160 Answers: 2 Comments: 1

solve : x^2 = 3x + 6y ; xy = 5x + 4y

$${solve}\::\:{x}^{\mathrm{2}} \:=\:\mathrm{3}{x}\:+\:\mathrm{6}{y}\:;\:{xy}\:=\:\mathrm{5}{x}\:+\:\mathrm{4}{y} \\ $$

Question Number 88153 Answers: 0 Comments: 1

Question Number 88141 Answers: 1 Comments: 0

Question Number 88137 Answers: 1 Comments: 2

Mr mjs x, 3,7,13,27,33,y find x & y ? any formula to generally?

$${Mr}\:{mjs}\: \\ $$$${x},\:\mathrm{3},\mathrm{7},\mathrm{13},\mathrm{27},\mathrm{33},{y} \\ $$$${find}\:{x}\:\&\:{y}\:?\:{any}\:{formula} \\ $$$${to}\:{generally}? \\ $$

Question Number 88131 Answers: 1 Comments: 0

∫((x^2 +1)/(x−(√(1−2x))))dx

$$\int\frac{{x}^{\mathrm{2}} +\mathrm{1}}{{x}−\sqrt{\mathrm{1}−\mathrm{2}{x}}}{dx} \\ $$

Question Number 91093 Answers: 0 Comments: 16

dear admint Tinkutara. why my phone nothing have notification sir?

$${dear}\:{admint}\: \\ $$$${Tinkutara}.\:{why}\:{my}\:{phone} \\ $$$${nothing}\:{have}\:{notification}\:{sir}? \\ $$$$ \\ $$

Question Number 88128 Answers: 1 Comments: 0

given 27^a = 64^b = 216^c = 72 find ((2020abc)/(3ab+3ac+3bc)) + ((ab+ac+bc)/(2020abc))

$${given}\:\mathrm{27}^{{a}} \:=\:\mathrm{64}^{{b}} \:=\:\mathrm{216}^{{c}} \:=\:\mathrm{72} \\ $$$${find}\:\frac{\mathrm{2020}{abc}}{\mathrm{3}{ab}+\mathrm{3}{ac}+\mathrm{3}{bc}}\:+\:\frac{{ab}+{ac}+{bc}}{\mathrm{2020}{abc}} \\ $$

Question Number 88118 Answers: 1 Comments: 1

∫(dx/((x+1)×(√x)))

$$\int\frac{\mathrm{dx}}{\left(\mathrm{x}+\mathrm{1}\right)×\sqrt{\mathrm{x}}} \\ $$

Question Number 88104 Answers: 1 Comments: 2

∫_0 ^(+∞) (√(3+e^(−2x) ))dx

$$\int_{\mathrm{0}} ^{+\infty} \sqrt{\mathrm{3}+{e}^{−\mathrm{2}{x}} }{dx} \\ $$

Question Number 88101 Answers: 0 Comments: 0

Question Number 88098 Answers: 0 Comments: 2

lim_(x→0^+ ) ((1/x)−(1/(sin x)))

$$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\left(\frac{\mathrm{1}}{{x}}−\frac{\mathrm{1}}{\mathrm{sin}\:{x}}\right) \\ $$

Question Number 88097 Answers: 1 Comments: 0

∫(dx/((2x−3)^(2/3) ))

$$\int\frac{\mathrm{dx}}{\left(\mathrm{2x}−\mathrm{3}\right)^{\frac{\mathrm{2}}{\mathrm{3}}} } \\ $$

Question Number 88092 Answers: 2 Comments: 3

lim_(x→0^+ ) ((1/x)−(1/(sin x)))

$$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\left(\frac{\mathrm{1}}{{x}}−\frac{\mathrm{1}}{\mathrm{sin}\:{x}}\right) \\ $$

Question Number 88089 Answers: 1 Comments: 1

∫(e^x /(e^2 −9))dx

$$\int\frac{{e}^{{x}} }{{e}^{\mathrm{2}} −\mathrm{9}}{dx} \\ $$

Question Number 88088 Answers: 0 Comments: 0

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