Optimal. Leaf size=20 \[ \frac{(x+1)^{3/2}}{3 (1-x)^{3/2}} \]
[Out]
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Rubi [A] time = 0.011888, antiderivative size = 20, 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 \[ \frac{(x+1)^{3/2}}{3 (1-x)^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[1 + x]/(1 - x)^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 2.51115, size = 14, normalized size = 0.7 \[ \frac{\left (x + 1\right )^{\frac{3}{2}}}{3 \left (- x + 1\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+x)**(1/2)/(1-x)**(5/2),x)
[Out]
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Mathematica [A] time = 0.017617, size = 20, normalized size = 1. \[ \frac{(x+1)^{3/2}}{3 (1-x)^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[1 + x]/(1 - x)^(5/2),x]
[Out]
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Maple [A] time = 0.006, size = 15, normalized size = 0.8 \[{\frac{1}{3} \left ( 1+x \right ) ^{{\frac{3}{2}}} \left ( 1-x \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+x)^(1/2)/(1-x)^(5/2),x)
[Out]
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Maxima [A] time = 1.33976, size = 51, normalized size = 2.55 \[ \frac{2 \, \sqrt{-x^{2} + 1}}{3 \,{\left (x^{2} - 2 \, x + 1\right )}} + \frac{\sqrt{-x^{2} + 1}}{3 \,{\left (x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x + 1)/(-x + 1)^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.205381, size = 76, normalized size = 3.8 \[ \frac{2 \,{\left (x^{3} + 3 \, \sqrt{x + 1} x \sqrt{-x + 1} - 3 \, x\right )}}{3 \,{\left (x^{3} -{\left (x^{2} - 3 \, x + 2\right )} \sqrt{x + 1} \sqrt{-x + 1} - 3 \, x + 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x + 1)/(-x + 1)^(5/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 10.0849, size = 61, normalized size = 3.05 \[ \begin{cases} \frac{i \left (x + 1\right )^{\frac{3}{2}}}{3 \sqrt{x - 1} \left (x + 1\right ) - 6 \sqrt{x - 1}} & \text{for}\: \frac{\left |{x + 1}\right |}{2} > 1 \\- \frac{\left (x + 1\right )^{\frac{3}{2}}}{3 \sqrt{- x + 1} \left (x + 1\right ) - 6 \sqrt{- x + 1}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1+x)**(1/2)/(1-x)**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.209565, size = 26, normalized size = 1.3 \[ \frac{{\left (x + 1\right )}^{\frac{3}{2}} \sqrt{-x + 1}}{3 \,{\left (x - 1\right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x + 1)/(-x + 1)^(5/2),x, algorithm="giac")
[Out]