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Question Number 61479 Answers: 3 Comments: 1

Solve for x: ((6(√(2x)))/(x − 1)) + ((5(√(x − 1)))/(2x)) = 13

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}:\:\:\:\:\:\:\:\frac{\mathrm{6}\sqrt{\mathrm{2x}}}{\mathrm{x}\:−\:\mathrm{1}}\:+\:\frac{\mathrm{5}\sqrt{\mathrm{x}\:−\:\mathrm{1}}}{\mathrm{2x}}\:\:\:=\:\:\mathrm{13} \\ $$

Question Number 61470 Answers: 1 Comments: 0

Is there any other solution besides {x=a,y=b} or {x=b,y=a} of the following system of equations x+y=a+b ∧ x^7 +y^7 =a^7 +b^7 ?

$$\mathrm{Is}\:\mathrm{there}\:\mathrm{any}\:\mathrm{other}\:\mathrm{solution}\:\mathrm{besides} \\ $$$$\left\{\mathrm{x}=\mathrm{a},\mathrm{y}=\mathrm{b}\right\}\:\mathrm{or}\:\left\{\mathrm{x}=\mathrm{b},\mathrm{y}=\mathrm{a}\right\}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{following}\:\mathrm{system}\:\mathrm{of}\:\mathrm{equations} \\ $$$$\:\:\:\:\mathrm{x}+\mathrm{y}=\mathrm{a}+\mathrm{b}\:\:\wedge\:\mathrm{x}^{\mathrm{7}} +\mathrm{y}^{\mathrm{7}} =\mathrm{a}^{\mathrm{7}} +\mathrm{b}^{\mathrm{7}} \:\:? \\ $$$$ \\ $$

Question Number 61465 Answers: 1 Comments: 1

∫_0 ^(2π) (1/(a^2 cos^2 (t)+b^2 sin^2 (t)))dt=((2π)/(ab))?

$$\int_{\mathrm{0}} ^{\mathrm{2}\pi} \frac{\mathrm{1}}{{a}^{\mathrm{2}} {cos}^{\mathrm{2}} \left({t}\right)+{b}^{\mathrm{2}} {sin}^{\mathrm{2}} \left({t}\right)}{dt}=\frac{\mathrm{2}\pi}{{ab}}? \\ $$

Question Number 61461 Answers: 1 Comments: 0

Question Number 61453 Answers: 1 Comments: 0

find ∫_0 ^1 ((ln(x)ln(1+x))/x)dx

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

Question Number 61451 Answers: 0 Comments: 0

Question Number 61449 Answers: 1 Comments: 1

Question Number 61425 Answers: 0 Comments: 1

Question Number 61424 Answers: 1 Comments: 0

Question Number 61412 Answers: 0 Comments: 2

Find the multinomial coefficient: ((( 9)),((3, 5, 1, 0)) )

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{multinomial}\:\mathrm{coefficient}:\:\:\:\:\:\begin{pmatrix}{\:\:\:\:\:\:\:\:\:\mathrm{9}}\\{\mathrm{3},\:\:\mathrm{5},\:\:\mathrm{1},\:\:\mathrm{0}}\end{pmatrix} \\ $$

Question Number 61408 Answers: 1 Comments: 0

∫_0 ^π (x/(tan^2 (x)−1)) dx

$$\int_{\mathrm{0}} ^{\pi} \frac{{x}}{{tan}^{\mathrm{2}} \left({x}\right)−\mathrm{1}}\:{dx} \\ $$

Question Number 61402 Answers: 0 Comments: 0

Question Number 61391 Answers: 0 Comments: 2

what is the best book for learning advanced calculus ?

$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{best}\:\mathrm{book}\:\mathrm{for}\:\mathrm{learning}\:\mathrm{advanced} \\ $$$$\mathrm{calculus}\:? \\ $$

Question Number 61388 Answers: 0 Comments: 5

calculate ∫_0 ^1 ((sin(lnx))/(lnx)) dx .

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{sin}\left({lnx}\right)}{{lnx}}\:{dx}\:. \\ $$

Question Number 61386 Answers: 0 Comments: 3

find the value of ∫_(−∞) ^(+∞) ((ln(1+x^2 ))/(1+x^2 )) dx

$${find}\:{the}\:{value}\:{of}\:\int_{−\infty} ^{+\infty} \:\:\frac{{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx} \\ $$

Question Number 61378 Answers: 0 Comments: 0

Solve the differential equation: (dy/dx) = x^2 + y^2

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation}:\:\:\frac{\mathrm{dy}}{\mathrm{dx}}\:\:=\:\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \\ $$

Question Number 61377 Answers: 0 Comments: 0

Find the multinomial coefficient: ((( 9)),((3, 5, 1, 0)) )

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{multinomial}\:\mathrm{coefficient}:\:\:\:\:\:\:\begin{pmatrix}{\:\:\:\:\:\:\:\mathrm{9}}\\{\mathrm{3},\:\mathrm{5},\:\mathrm{1},\:\mathrm{0}}\end{pmatrix} \\ $$

Question Number 61363 Answers: 1 Comments: 0

Question Number 61349 Answers: 1 Comments: 7

Question Number 61347 Answers: 2 Comments: 1

Question Number 61343 Answers: 1 Comments: 0

Question Number 61335 Answers: 1 Comments: 0

Question Number 61329 Answers: 0 Comments: 2

let f(x) =(e^(−x) /(1+x)) sin(3x) 1) dtermine f^((n)) (x) and f^((n)) (0) 2) developp f at integr serie .

$${let}\:{f}\left({x}\right)\:=\frac{{e}^{−{x}} }{\mathrm{1}+{x}}\:{sin}\left(\mathrm{3}{x}\right) \\ $$$$\left.\mathrm{1}\right)\:{dtermine}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}\:. \\ $$

Question Number 61328 Answers: 0 Comments: 4

let f(a) =∫_0 ^1 ((sin(2x))/(1+ax^2 )) dx with ∣a∣<1 1) approximate f(a) by a polynom 2) find the value (perhaps not exact) of ∫_0 ^1 ((sin(2x))/(1+2x^2 )) dx 3) let g(a) = ∫_0 ^1 ((x^2 sin(2x))/((1+ax^2 )^2 )) dx approximat g(a) by a polynom 4) find the value of ∫_0 ^1 ((x^2 sin(2x))/((1+2x^2 )^2 )) dx .

$${let}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{sin}\left(\mathrm{2}{x}\right)}{\mathrm{1}+{ax}^{\mathrm{2}} }\:{dx}\:\:{with}\:\:\mid{a}\mid<\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{approximate}\:{f}\left({a}\right)\:{by}\:{a}\:{polynom} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:\:\left({perhaps}\:{not}\:{exact}\right)\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{sin}\left(\mathrm{2}{x}\right)}{\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} }\:{dx} \\ $$$$\left.\mathrm{3}\right)\:{let}\:{g}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{x}^{\mathrm{2}} {sin}\left(\mathrm{2}{x}\right)}{\left(\mathrm{1}+{ax}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{dx}\:\:\:{approximat}\:{g}\left({a}\right)\:{by}\:{a}\:{polynom} \\ $$$$\left.\mathrm{4}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{x}^{\mathrm{2}} {sin}\left(\mathrm{2}{x}\right)}{\left(\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{dx}\:. \\ $$

Question Number 61327 Answers: 1 Comments: 0

Question Number 61326 Answers: 0 Comments: 4

find ∫_0 ^1 ((sinx)/(1+x^2 ))dx

$${find}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{sinx}}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$

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