Optimal. Leaf size=81 \[ \frac{2 (x+1)^{7/2}}{3003 (1-x)^{7/2}}+\frac{2 (x+1)^{7/2}}{429 (1-x)^{9/2}}+\frac{3 (x+1)^{7/2}}{143 (1-x)^{11/2}}+\frac{(x+1)^{7/2}}{13 (1-x)^{13/2}} \]
[Out]
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Rubi [A] time = 0.0531703, 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 \[ \frac{2 (x+1)^{7/2}}{3003 (1-x)^{7/2}}+\frac{2 (x+1)^{7/2}}{429 (1-x)^{9/2}}+\frac{3 (x+1)^{7/2}}{143 (1-x)^{11/2}}+\frac{(x+1)^{7/2}}{13 (1-x)^{13/2}} \]
Antiderivative was successfully verified.
[In] Int[(1 + x)^(5/2)/(1 - x)^(15/2),x]
[Out]
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Rubi in Sympy [A] time = 6.90044, size = 65, normalized size = 0.8 \[ \frac{2 \left (x + 1\right )^{\frac{7}{2}}}{3003 \left (- x + 1\right )^{\frac{7}{2}}} + \frac{2 \left (x + 1\right )^{\frac{7}{2}}}{429 \left (- x + 1\right )^{\frac{9}{2}}} + \frac{3 \left (x + 1\right )^{\frac{7}{2}}}{143 \left (- x + 1\right )^{\frac{11}{2}}} + \frac{\left (x + 1\right )^{\frac{7}{2}}}{13 \left (- x + 1\right )^{\frac{13}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+x)**(5/2)/(1-x)**(15/2),x)
[Out]
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Mathematica [A] time = 0.0254316, size = 40, normalized size = 0.49 \[ \frac{(x+1)^3 \sqrt{1-x^2} \left (2 x^3-20 x^2+97 x-310\right )}{3003 (x-1)^7} \]
Antiderivative was successfully verified.
[In] Integrate[(1 + x)^(5/2)/(1 - x)^(15/2),x]
[Out]
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Maple [A] time = 0.003, size = 30, normalized size = 0.4 \[ -{\frac{2\,{x}^{3}-20\,{x}^{2}+97\,x-310}{3003} \left ( 1+x \right ) ^{{\frac{7}{2}}} \left ( 1-x \right ) ^{-{\frac{13}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+x)^(5/2)/(1-x)^(15/2),x)
[Out]
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Maxima [A] time = 1.3386, size = 439, normalized size = 5.42 \[ -\frac{{\left (-x^{2} + 1\right )}^{\frac{5}{2}}}{4 \,{\left (x^{9} - 9 \, x^{8} + 36 \, x^{7} - 84 \, x^{6} + 126 \, x^{5} - 126 \, x^{4} + 84 \, x^{3} - 36 \, x^{2} + 9 \, x - 1\right )}} - \frac{{\left (-x^{2} + 1\right )}^{\frac{3}{2}}}{4 \,{\left (x^{8} - 8 \, x^{7} + 28 \, x^{6} - 56 \, x^{5} + 70 \, x^{4} - 56 \, x^{3} + 28 \, x^{2} - 8 \, x + 1\right )}} - \frac{3 \, \sqrt{-x^{2} + 1}}{26 \,{\left (x^{7} - 7 \, x^{6} + 21 \, x^{5} - 35 \, x^{4} + 35 \, x^{3} - 21 \, x^{2} + 7 \, x - 1\right )}} - \frac{3 \, \sqrt{-x^{2} + 1}}{572 \,{\left (x^{6} - 6 \, x^{5} + 15 \, x^{4} - 20 \, x^{3} + 15 \, x^{2} - 6 \, x + 1\right )}} + \frac{5 \, \sqrt{-x^{2} + 1}}{1716 \,{\left (x^{5} - 5 \, x^{4} + 10 \, x^{3} - 10 \, x^{2} + 5 \, x - 1\right )}} - \frac{5 \, \sqrt{-x^{2} + 1}}{3003 \,{\left (x^{4} - 4 \, x^{3} + 6 \, x^{2} - 4 \, x + 1\right )}} + \frac{\sqrt{-x^{2} + 1}}{1001 \,{\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )}} - \frac{2 \, \sqrt{-x^{2} + 1}}{3003 \,{\left (x^{2} - 2 \, x + 1\right )}} + \frac{2 \, \sqrt{-x^{2} + 1}}{3003 \,{\left (x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)^(5/2)/(-x + 1)^(15/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.208693, size = 358, normalized size = 4.42 \[ \frac{308 \, x^{13} - 4030 \, x^{12} + 12181 \, x^{11} + 11726 \, x^{10} - 123838 \, x^{9} + 220506 \, x^{8} - 6435 \, x^{7} - 498498 \, x^{6} + 528528 \, x^{5} - 240240 \, x^{3} + 288288 \, x^{2} + 13 \,{\left (24 \, x^{12} - 2 \, x^{11} - 1067 \, x^{10} + 4345 \, x^{9} - 4719 \, x^{8} - 8283 \, x^{7} + 30030 \, x^{6} - 25872 \, x^{5} - 11088 \, x^{4} + 25872 \, x^{3} - 22176 \, x^{2} + 14784 \, x\right )} \sqrt{x + 1} \sqrt{-x + 1} - 192192 \, x}{3003 \,{\left (x^{13} - 13 \, x^{12} + 39 \, x^{11} + 39 \, x^{10} - 403 \, x^{9} + 689 \, x^{8} + 13 \, x^{7} - 1443 \, x^{6} + 1742 \, x^{5} - 312 \, x^{4} - 1040 \, x^{3} + 1040 \, x^{2} +{\left (x^{12} - 45 \, x^{10} + 182 \, x^{9} - 193 \, x^{8} - 364 \, x^{7} + 1189 \, x^{6} - 1066 \, x^{5} - 232 \, x^{4} + 1248 \, x^{3} - 1072 \, x^{2} + 416 \, x - 64\right )} \sqrt{x + 1} \sqrt{-x + 1} - 416 \, x + 64\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)^(5/2)/(-x + 1)^(15/2),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)**(15/2),x)
[Out]
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GIAC/XCAS [A] time = 0.224477, size = 47, normalized size = 0.58 \[ \frac{{\left ({\left (2 \,{\left (x + 1\right )}{\left (x - 12\right )} + 143\right )}{\left (x + 1\right )} - 429\right )}{\left (x + 1\right )}^{\frac{7}{2}} \sqrt{-x + 1}}{3003 \,{\left (x - 1\right )}^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)^(5/2)/(-x + 1)^(15/2),x, algorithm="giac")
[Out]