Optimal. Leaf size=61 \[ \frac{2 (x+1)^{5/2}}{315 (1-x)^{5/2}}+\frac{2 (x+1)^{5/2}}{63 (1-x)^{7/2}}+\frac{(x+1)^{5/2}}{9 (1-x)^{9/2}} \]
[Out]
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Rubi [A] time = 0.0374626, antiderivative size = 61, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ \frac{2 (x+1)^{5/2}}{315 (1-x)^{5/2}}+\frac{2 (x+1)^{5/2}}{63 (1-x)^{7/2}}+\frac{(x+1)^{5/2}}{9 (1-x)^{9/2}} \]
Antiderivative was successfully verified.
[In] Int[(1 + x)^(3/2)/(1 - x)^(11/2),x]
[Out]
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Rubi in Sympy [A] time = 5.12022, size = 48, normalized size = 0.79 \[ \frac{2 \left (x + 1\right )^{\frac{5}{2}}}{315 \left (- x + 1\right )^{\frac{5}{2}}} + \frac{2 \left (x + 1\right )^{\frac{5}{2}}}{63 \left (- x + 1\right )^{\frac{7}{2}}} + \frac{\left (x + 1\right )^{\frac{5}{2}}}{9 \left (- x + 1\right )^{\frac{9}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+x)**(3/2)/(1-x)**(11/2),x)
[Out]
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Mathematica [A] time = 0.0214625, size = 35, normalized size = 0.57 \[ -\frac{(x+1)^2 \sqrt{1-x^2} \left (2 x^2-14 x+47\right )}{315 (x-1)^5} \]
Antiderivative was successfully verified.
[In] Integrate[(1 + x)^(3/2)/(1 - x)^(11/2),x]
[Out]
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Maple [A] time = 0.004, size = 25, normalized size = 0.4 \[{\frac{2\,{x}^{2}-14\,x+47}{315} \left ( 1+x \right ) ^{{\frac{5}{2}}} \left ( 1-x \right ) ^{-{\frac{9}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+x)^(3/2)/(1-x)^(11/2),x)
[Out]
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Maxima [A] time = 1.34682, size = 232, normalized size = 3.8 \[ \frac{{\left (-x^{2} + 1\right )}^{\frac{3}{2}}}{3 \,{\left (x^{6} - 6 \, x^{5} + 15 \, x^{4} - 20 \, x^{3} + 15 \, x^{2} - 6 \, x + 1\right )}} + \frac{2 \, \sqrt{-x^{2} + 1}}{9 \,{\left (x^{5} - 5 \, x^{4} + 10 \, x^{3} - 10 \, x^{2} + 5 \, x - 1\right )}} + \frac{\sqrt{-x^{2} + 1}}{63 \,{\left (x^{4} - 4 \, x^{3} + 6 \, x^{2} - 4 \, x + 1\right )}} - \frac{\sqrt{-x^{2} + 1}}{105 \,{\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )}} + \frac{2 \, \sqrt{-x^{2} + 1}}{315 \,{\left (x^{2} - 2 \, x + 1\right )}} - \frac{2 \, \sqrt{-x^{2} + 1}}{315 \,{\left (x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)^(3/2)/(-x + 1)^(11/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.203186, size = 257, normalized size = 4.21 \[ \frac{49 \, x^{9} - 423 \, x^{8} + 801 \, x^{7} + 1071 \, x^{6} - 4158 \, x^{5} + 3780 \, x^{4} - 840 \, x^{3} - 5040 \, x^{2} + 3 \,{\left (15 \, x^{8} + 6 \, x^{7} - 357 \, x^{6} + 896 \, x^{5} - 420 \, x^{4} - 560 \, x^{3} + 1680 \, x^{2} - 1680 \, x\right )} \sqrt{x + 1} \sqrt{-x + 1} + 5040 \, x}{315 \,{\left (x^{9} - 9 \, x^{8} + 18 \, x^{7} + 18 \, x^{6} - 99 \, x^{5} + 99 \, x^{4} + 24 \, x^{3} - 108 \, x^{2} +{\left (x^{8} - 22 \, x^{6} + 60 \, x^{5} - 39 \, x^{4} - 60 \, x^{3} + 116 \, x^{2} - 72 \, x + 16\right )} \sqrt{x + 1} \sqrt{-x + 1} + 72 \, x - 16\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)^(3/2)/(-x + 1)^(11/2),x, algorithm="fricas")
[Out]
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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+x)**(3/2)/(1-x)**(11/2),x)
[Out]
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GIAC/XCAS [A] time = 0.215412, size = 39, normalized size = 0.64 \[ -\frac{{\left (2 \,{\left (x + 1\right )}{\left (x - 8\right )} + 63\right )}{\left (x + 1\right )}^{\frac{5}{2}} \sqrt{-x + 1}}{315 \,{\left (x - 1\right )}^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)^(3/2)/(-x + 1)^(11/2),x, algorithm="giac")
[Out]