Optimal. Leaf size=81 \[ \frac{2 (x+1)^{5/2}}{1155 (1-x)^{5/2}}+\frac{2 (x+1)^{5/2}}{231 (1-x)^{7/2}}+\frac{(x+1)^{5/2}}{33 (1-x)^{9/2}}+\frac{(x+1)^{5/2}}{11 (1-x)^{11/2}} \]
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Rubi [A] time = 0.0529028, antiderivative size = 81, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ \frac{2 (x+1)^{5/2}}{1155 (1-x)^{5/2}}+\frac{2 (x+1)^{5/2}}{231 (1-x)^{7/2}}+\frac{(x+1)^{5/2}}{33 (1-x)^{9/2}}+\frac{(x+1)^{5/2}}{11 (1-x)^{11/2}} \]
Antiderivative was successfully verified.
[In] Int[(1 + x)^(3/2)/(1 - x)^(13/2),x]
[Out]
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Rubi in Sympy [A] time = 6.73669, size = 63, normalized size = 0.78 \[ \frac{2 \left (x + 1\right )^{\frac{5}{2}}}{1155 \left (- x + 1\right )^{\frac{5}{2}}} + \frac{2 \left (x + 1\right )^{\frac{5}{2}}}{231 \left (- x + 1\right )^{\frac{7}{2}}} + \frac{\left (x + 1\right )^{\frac{5}{2}}}{33 \left (- x + 1\right )^{\frac{9}{2}}} + \frac{\left (x + 1\right )^{\frac{5}{2}}}{11 \left (- x + 1\right )^{\frac{11}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+x)**(3/2)/(1-x)**(13/2),x)
[Out]
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Mathematica [A] time = 0.0237805, size = 40, normalized size = 0.49 \[ -\frac{(x+1)^2 \sqrt{1-x^2} \left (2 x^3-16 x^2+61 x-152\right )}{1155 (x-1)^6} \]
Warning: Unable to verify antiderivative.
[In] Integrate[(1 + x)^(3/2)/(1 - x)^(13/2),x]
[Out]
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Maple [A] time = 0.005, size = 30, normalized size = 0.4 \[ -{\frac{2\,{x}^{3}-16\,{x}^{2}+61\,x-152}{1155} \left ( 1+x \right ) ^{{\frac{5}{2}}} \left ( 1-x \right ) ^{-{\frac{11}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+x)^(3/2)/(1-x)^(13/2),x)
[Out]
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Maxima [A] time = 1.35981, size = 294, normalized size = 3.63 \[ -\frac{{\left (-x^{2} + 1\right )}^{\frac{3}{2}}}{4 \,{\left (x^{7} - 7 \, x^{6} + 21 \, x^{5} - 35 \, x^{4} + 35 \, x^{3} - 21 \, x^{2} + 7 \, x - 1\right )}} - \frac{3 \, \sqrt{-x^{2} + 1}}{22 \,{\left (x^{6} - 6 \, x^{5} + 15 \, x^{4} - 20 \, x^{3} + 15 \, x^{2} - 6 \, x + 1\right )}} - \frac{\sqrt{-x^{2} + 1}}{132 \,{\left (x^{5} - 5 \, x^{4} + 10 \, x^{3} - 10 \, x^{2} + 5 \, x - 1\right )}} + \frac{\sqrt{-x^{2} + 1}}{231 \,{\left (x^{4} - 4 \, x^{3} + 6 \, x^{2} - 4 \, x + 1\right )}} - \frac{\sqrt{-x^{2} + 1}}{385 \,{\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )}} + \frac{2 \, \sqrt{-x^{2} + 1}}{1155 \,{\left (x^{2} - 2 \, x + 1\right )}} - \frac{2 \, \sqrt{-x^{2} + 1}}{1155 \,{\left (x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)^(3/2)/(-x + 1)^(13/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214296, size = 312, normalized size = 3.85 \[ \frac{150 \, x^{11} + 22 \, x^{10} - 5071 \, x^{9} + 16665 \, x^{8} - 10989 \, x^{7} - 35343 \, x^{6} + 66066 \, x^{5} - 32340 \, x^{4} - 18480 \, x^{3} + 55440 \, x^{2} - 11 \,{\left (14 \, x^{10} - 152 \, x^{9} + 381 \, x^{8} + 324 \, x^{7} - 2793 \, x^{6} + 3906 \, x^{5} - 420 \, x^{4} - 3360 \, x^{3} + 5040 \, x^{2} - 3360 \, x\right )} \sqrt{x + 1} \sqrt{-x + 1} - 36960 \, x}{1155 \,{\left (x^{11} - 33 \, x^{9} + 110 \, x^{8} - 77 \, x^{7} - 220 \, x^{6} + 473 \, x^{5} - 242 \, x^{4} - 220 \, x^{3} + 352 \, x^{2} -{\left (x^{10} - 11 \, x^{9} + 28 \, x^{8} + 22 \, x^{7} - 199 \, x^{6} + 297 \, x^{5} - 54 \, x^{4} - 308 \, x^{3} + 368 \, x^{2} - 176 \, x + 32\right )} \sqrt{x + 1} \sqrt{-x + 1} - 176 \, x + 32\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)^(3/2)/(-x + 1)^(13/2),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)**(13/2),x)
[Out]
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GIAC/XCAS [A] time = 0.215264, size = 47, normalized size = 0.58 \[ -\frac{{\left ({\left (2 \,{\left (x + 1\right )}{\left (x - 10\right )} + 99\right )}{\left (x + 1\right )} - 231\right )}{\left (x + 1\right )}^{\frac{5}{2}} \sqrt{-x + 1}}{1155 \,{\left (x - 1\right )}^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)^(3/2)/(-x + 1)^(13/2),x, algorithm="giac")
[Out]