Optimal. Leaf size=37 \[ \frac{2}{\sqrt{3-x} \sqrt{x-2}}-\frac{4 \sqrt{3-x}}{\sqrt{x-2}} \]
[Out]
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Rubi [A] time = 0.0257071, antiderivative size = 37, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ \frac{2}{\sqrt{3-x} \sqrt{x-2}}-\frac{4 \sqrt{3-x}}{\sqrt{x-2}} \]
Antiderivative was successfully verified.
[In] Int[1/((3 - x)^(3/2)*(-2 + x)^(3/2)),x]
[Out]
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Rubi in Sympy [A] time = 3.64084, size = 29, normalized size = 0.78 \[ \frac{4 \sqrt{x - 2}}{\sqrt{- x + 3}} - \frac{2}{\sqrt{- x + 3} \sqrt{x - 2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(3-x)**(3/2)/(-2+x)**(3/2),x)
[Out]
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Mathematica [A] time = 0.013086, size = 21, normalized size = 0.57 \[ \frac{2 (2 x-5)}{\sqrt{-x^2+5 x-6}} \]
Antiderivative was successfully verified.
[In] Integrate[1/((3 - x)^(3/2)*(-2 + x)^(3/2)),x]
[Out]
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Maple [A] time = 0.004, size = 20, normalized size = 0.5 \[ 2\,{\frac{-5+2\,x}{\sqrt{3-x}\sqrt{-2+x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(3-x)^(3/2)/(-2+x)^(3/2),x)
[Out]
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Maxima [A] time = 1.33223, size = 41, normalized size = 1.11 \[ \frac{4 \, x}{\sqrt{-x^{2} + 5 \, x - 6}} - \frac{10}{\sqrt{-x^{2} + 5 \, x - 6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x - 2)^(3/2)*(-x + 3)^(3/2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.207504, size = 39, normalized size = 1.05 \[ -\frac{2 \,{\left (2 \, x - 5\right )} \sqrt{x - 2} \sqrt{-x + 3}}{x^{2} - 5 \, x + 6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x - 2)^(3/2)*(-x + 3)^(3/2)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 13.3961, size = 100, normalized size = 2.7 \[ \begin{cases} - \frac{4 i \sqrt{x - 3} \left (x - 2\right )}{\left (x - 2\right )^{\frac{3}{2}} - \sqrt{x - 2}} + \frac{2 i \sqrt{x - 3}}{\left (x - 2\right )^{\frac{3}{2}} - \sqrt{x - 2}} & \text{for}\: \left |{x - 2}\right | > 1 \\- \frac{4 \sqrt{- x + 3} \left (x - 2\right )}{\left (x - 2\right )^{\frac{3}{2}} - \sqrt{x - 2}} + \frac{2 \sqrt{- x + 3}}{\left (x - 2\right )^{\frac{3}{2}} - \sqrt{x - 2}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(3-x)**(3/2)/(-2+x)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.220804, size = 72, normalized size = 1.95 \[ -\frac{\sqrt{-x + 3} - 1}{\sqrt{x - 2}} - \frac{2 \, \sqrt{x - 2} \sqrt{-x + 3}}{x - 3} + \frac{\sqrt{x - 2}}{\sqrt{-x + 3} - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x - 2)^(3/2)*(-x + 3)^(3/2)),x, algorithm="giac")
[Out]