Optimal. Leaf size=41 \[ \frac{(x+1)^{7/2}}{63 (1-x)^{7/2}}+\frac{(x+1)^{7/2}}{9 (1-x)^{9/2}} \]
[Out]
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Rubi [A] time = 0.0242483, antiderivative size = 41, 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 \[ \frac{(x+1)^{7/2}}{63 (1-x)^{7/2}}+\frac{(x+1)^{7/2}}{9 (1-x)^{9/2}} \]
Antiderivative was successfully verified.
[In] Int[(1 + x)^(5/2)/(1 - x)^(11/2),x]
[Out]
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Rubi in Sympy [A] time = 3.65636, size = 29, normalized size = 0.71 \[ \frac{\left (x + 1\right )^{\frac{7}{2}}}{63 \left (- x + 1\right )^{\frac{7}{2}}} + \frac{\left (x + 1\right )^{\frac{7}{2}}}{9 \left (- x + 1\right )^{\frac{9}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+x)**(5/2)/(1-x)**(11/2),x)
[Out]
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Mathematica [A] time = 0.0209838, size = 28, normalized size = 0.68 \[ \frac{(x-8) (x+1)^3 \sqrt{1-x^2}}{63 (x-1)^5} \]
Warning: Unable to verify antiderivative.
[In] Integrate[(1 + x)^(5/2)/(1 - x)^(11/2),x]
[Out]
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Maple [A] time = 0.003, size = 18, normalized size = 0.4 \[ -{\frac{x-8}{63} \left ( 1+x \right ) ^{{\frac{7}{2}}} \left ( 1-x \right ) ^{-{\frac{9}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+x)^(5/2)/(1-x)^(11/2),x)
[Out]
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Maxima [A] time = 1.35548, size = 294, normalized size = 7.17 \[ -\frac{{\left (-x^{2} + 1\right )}^{\frac{5}{2}}}{2 \,{\left (x^{7} - 7 \, x^{6} + 21 \, x^{5} - 35 \, x^{4} + 35 \, x^{3} - 21 \, x^{2} + 7 \, x - 1\right )}} - \frac{5 \,{\left (-x^{2} + 1\right )}^{\frac{3}{2}}}{6 \,{\left (x^{6} - 6 \, x^{5} + 15 \, x^{4} - 20 \, x^{3} + 15 \, x^{2} - 6 \, x + 1\right )}} - \frac{5 \, \sqrt{-x^{2} + 1}}{9 \,{\left (x^{5} - 5 \, x^{4} + 10 \, x^{3} - 10 \, x^{2} + 5 \, x - 1\right )}} - \frac{5 \, \sqrt{-x^{2} + 1}}{126 \,{\left (x^{4} - 4 \, x^{3} + 6 \, x^{2} - 4 \, x + 1\right )}} + \frac{\sqrt{-x^{2} + 1}}{42 \,{\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )}} - \frac{\sqrt{-x^{2} + 1}}{63 \,{\left (x^{2} - 2 \, x + 1\right )}} + \frac{\sqrt{-x^{2} + 1}}{63 \,{\left (x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)^(5/2)/(-x + 1)^(11/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.207367, size = 250, normalized size = 6.1 \[ \frac{7 \, x^{9} - 72 \, x^{8} + 198 \, x^{7} + 252 \, x^{6} - 945 \, x^{5} + 252 \, x^{4} - 84 \, x^{3} - 504 \, x^{2} + 3 \,{\left (3 \, x^{8} - 3 \, x^{7} - 63 \, x^{6} + 203 \, x^{5} - 140 \, x^{3} + 168 \, x^{2} - 336 \, x\right )} \sqrt{x + 1} \sqrt{-x + 1} + 1008 \, x}{63 \,{\left (x^{9} - 9 \, x^{8} + 18 \, x^{7} + 18 \, x^{6} - 99 \, x^{5} + 99 \, x^{4} + 24 \, x^{3} - 108 \, x^{2} +{\left (x^{8} - 22 \, x^{6} + 60 \, x^{5} - 39 \, x^{4} - 60 \, x^{3} + 116 \, x^{2} - 72 \, x + 16\right )} \sqrt{x + 1} \sqrt{-x + 1} + 72 \, x - 16\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)^(5/2)/(-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)**(5/2)/(1-x)**(11/2),x)
[Out]
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GIAC/XCAS [A] time = 0.217918, size = 30, normalized size = 0.73 \[ \frac{{\left (x + 1\right )}^{\frac{7}{2}}{\left (x - 8\right )} \sqrt{-x + 1}}{63 \,{\left (x - 1\right )}^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)^(5/2)/(-x + 1)^(11/2),x, algorithm="giac")
[Out]