3.1167 \(\int \frac{1}{(6-2 x)^{3/2} (3+x)^{3/2}} \, dx\)

Optimal. Leaf size=26 \[ \frac{x}{18 \sqrt{2} \sqrt{3-x} \sqrt{x+3}} \]

[Out]

x/(18*Sqrt[2]*Sqrt[3 - x]*Sqrt[3 + x])

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Rubi [A]  time = 0.0148015, antiderivative size = 26, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ \frac{x}{18 \sqrt{2} \sqrt{3-x} \sqrt{x+3}} \]

Antiderivative was successfully verified.

[In]  Int[1/((6 - 2*x)^(3/2)*(3 + x)^(3/2)),x]

[Out]

x/(18*Sqrt[2]*Sqrt[3 - x]*Sqrt[3 + x])

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Rubi in Sympy [A]  time = 2.65766, size = 17, normalized size = 0.65 \[ \frac{x}{18 \sqrt{- 2 x + 6} \sqrt{x + 3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/(6-2*x)**(3/2)/(3+x)**(3/2),x)

[Out]

x/(18*sqrt(-2*x + 6)*sqrt(x + 3))

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Mathematica [A]  time = 0.0382908, size = 21, normalized size = 0.81 \[ \frac{x}{18 \sqrt{2} \sqrt{9-x^2}} \]

Antiderivative was successfully verified.

[In]  Integrate[1/((6 - 2*x)^(3/2)*(3 + x)^(3/2)),x]

[Out]

x/(18*Sqrt[2]*Sqrt[9 - x^2])

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Maple [A]  time = 0.003, size = 19, normalized size = 0.7 \[ -{\frac{ \left ( -3+x \right ) x}{9}{\frac{1}{\sqrt{3+x}}} \left ( 6-2\,x \right ) ^{-{\frac{3}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(6-2*x)^(3/2)/(3+x)^(3/2),x)

[Out]

-1/9*(-3+x)/(3+x)^(1/2)*x/(6-2*x)^(3/2)

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Maxima [A]  time = 1.34648, size = 16, normalized size = 0.62 \[ \frac{x}{18 \, \sqrt{-2 \, x^{2} + 18}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/((x + 3)^(3/2)*(-2*x + 6)^(3/2)),x, algorithm="maxima")

[Out]

1/18*x/sqrt(-2*x^2 + 18)

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Fricas [A]  time = 0.201888, size = 30, normalized size = 1.15 \[ -\frac{\sqrt{x + 3} x \sqrt{-2 \, x + 6}}{36 \,{\left (x^{2} - 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/((x + 3)^(3/2)*(-2*x + 6)^(3/2)),x, algorithm="fricas")

[Out]

-1/36*sqrt(x + 3)*x*sqrt(-2*x + 6)/(x^2 - 9)

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Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(6-2*x)**(3/2)/(3+x)**(3/2),x)

[Out]

Timed out

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GIAC/XCAS [A]  time = 0.222175, size = 96, normalized size = 3.69 \[ \frac{\sqrt{2}{\left (\sqrt{6} - \sqrt{-x + 3}\right )}}{144 \, \sqrt{x + 3}} - \frac{\sqrt{2} \sqrt{x + 3} \sqrt{-x + 3}}{72 \,{\left (x - 3\right )}} - \frac{\sqrt{2} \sqrt{x + 3}}{144 \,{\left (\sqrt{6} - \sqrt{-x + 3}\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/((x + 3)^(3/2)*(-2*x + 6)^(3/2)),x, algorithm="giac")

[Out]

1/144*sqrt(2)*(sqrt(6) - sqrt(-x + 3))/sqrt(x + 3) - 1/72*sqrt(2)*sqrt(x + 3)*sq
rt(-x + 3)/(x - 3) - 1/144*sqrt(2)*sqrt(x + 3)/(sqrt(6) - sqrt(-x + 3))