Optimal. Leaf size=101 \[ \frac{8 (x+1)^{7/2}}{45045 (1-x)^{7/2}}+\frac{8 (x+1)^{7/2}}{6435 (1-x)^{9/2}}+\frac{4 (x+1)^{7/2}}{715 (1-x)^{11/2}}+\frac{4 (x+1)^{7/2}}{195 (1-x)^{13/2}}+\frac{(x+1)^{7/2}}{15 (1-x)^{15/2}} \]
[Out]
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Rubi [A] time = 0.0695147, antiderivative size = 101, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ \frac{8 (x+1)^{7/2}}{45045 (1-x)^{7/2}}+\frac{8 (x+1)^{7/2}}{6435 (1-x)^{9/2}}+\frac{4 (x+1)^{7/2}}{715 (1-x)^{11/2}}+\frac{4 (x+1)^{7/2}}{195 (1-x)^{13/2}}+\frac{(x+1)^{7/2}}{15 (1-x)^{15/2}} \]
Antiderivative was successfully verified.
[In] Int[(1 + x)^(5/2)/(1 - x)^(17/2),x]
[Out]
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Rubi in Sympy [A] time = 8.60102, size = 82, normalized size = 0.81 \[ \frac{8 \left (x + 1\right )^{\frac{7}{2}}}{45045 \left (- x + 1\right )^{\frac{7}{2}}} + \frac{8 \left (x + 1\right )^{\frac{7}{2}}}{6435 \left (- x + 1\right )^{\frac{9}{2}}} + \frac{4 \left (x + 1\right )^{\frac{7}{2}}}{715 \left (- x + 1\right )^{\frac{11}{2}}} + \frac{4 \left (x + 1\right )^{\frac{7}{2}}}{195 \left (- x + 1\right )^{\frac{13}{2}}} + \frac{\left (x + 1\right )^{\frac{7}{2}}}{15 \left (- x + 1\right )^{\frac{15}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+x)**(5/2)/(1-x)**(17/2),x)
[Out]
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Mathematica [A] time = 0.0277988, size = 45, normalized size = 0.45 \[ \frac{(x+1)^3 \sqrt{1-x^2} \left (8 x^4-88 x^3+468 x^2-1628 x+4243\right )}{45045 (x-1)^8} \]
Warning: Unable to verify antiderivative.
[In] Integrate[(1 + x)^(5/2)/(1 - x)^(17/2),x]
[Out]
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Maple [A] time = 0.004, size = 35, normalized size = 0.4 \[{\frac{8\,{x}^{4}-88\,{x}^{3}+468\,{x}^{2}-1628\,x+4243}{45045} \left ( 1+x \right ) ^{{\frac{7}{2}}} \left ( 1-x \right ) ^{-{\frac{15}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+x)^(5/2)/(1-x)^(17/2),x)
[Out]
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Maxima [A] time = 1.34592, size = 521, normalized size = 5.16 \[ \frac{{\left (-x^{2} + 1\right )}^{\frac{5}{2}}}{5 \,{\left (x^{10} - 10 \, x^{9} + 45 \, x^{8} - 120 \, x^{7} + 210 \, x^{6} - 252 \, x^{5} + 210 \, x^{4} - 120 \, x^{3} + 45 \, x^{2} - 10 \, x + 1\right )}} + \frac{{\left (-x^{2} + 1\right )}^{\frac{3}{2}}}{6 \,{\left (x^{9} - 9 \, x^{8} + 36 \, x^{7} - 84 \, x^{6} + 126 \, x^{5} - 126 \, x^{4} + 84 \, x^{3} - 36 \, x^{2} + 9 \, x - 1\right )}} + \frac{\sqrt{-x^{2} + 1}}{15 \,{\left (x^{8} - 8 \, x^{7} + 28 \, x^{6} - 56 \, x^{5} + 70 \, x^{4} - 56 \, x^{3} + 28 \, x^{2} - 8 \, x + 1\right )}} + \frac{\sqrt{-x^{2} + 1}}{390 \,{\left (x^{7} - 7 \, x^{6} + 21 \, x^{5} - 35 \, x^{4} + 35 \, x^{3} - 21 \, x^{2} + 7 \, x - 1\right )}} - \frac{\sqrt{-x^{2} + 1}}{715 \,{\left (x^{6} - 6 \, x^{5} + 15 \, x^{4} - 20 \, x^{3} + 15 \, x^{2} - 6 \, x + 1\right )}} + \frac{\sqrt{-x^{2} + 1}}{1287 \,{\left (x^{5} - 5 \, x^{4} + 10 \, x^{3} - 10 \, x^{2} + 5 \, x - 1\right )}} - \frac{4 \, \sqrt{-x^{2} + 1}}{9009 \,{\left (x^{4} - 4 \, x^{3} + 6 \, x^{2} - 4 \, x + 1\right )}} + \frac{4 \, \sqrt{-x^{2} + 1}}{15015 \,{\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )}} - \frac{8 \, \sqrt{-x^{2} + 1}}{45045 \,{\left (x^{2} - 2 \, x + 1\right )}} + \frac{8 \, \sqrt{-x^{2} + 1}}{45045 \,{\left (x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)^(5/2)/(-x + 1)^(17/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.207872, size = 420, normalized size = 4.16 \[ \frac{4251 \, x^{15} - 120 \, x^{14} - 254160 \, x^{13} + 1188460 \, x^{12} - 1405755 \, x^{11} - 3543540 \, x^{10} + 12759890 \, x^{9} - 12097800 \, x^{8} - 9047610 \, x^{7} + 31231200 \, x^{6} - 21189168 \, x^{5} - 5765760 \, x^{4} + 13933920 \, x^{3} - 11531520 \, x^{2} -{\left (4235 \, x^{14} - 63645 \, x^{13} + 225355 \, x^{12} + 188695 \, x^{11} - 2835690 \, x^{10} + 6221072 \, x^{9} - 2247960 \, x^{8} - 12615174 \, x^{7} + 24024000 \, x^{6} - 12060048 \, x^{5} - 11531520 \, x^{4} + 16816800 \, x^{3} - 11531520 \, x^{2} + 5765760 \, x\right )} \sqrt{x + 1} \sqrt{-x + 1} + 5765760 \, x}{45045 \,{\left (x^{15} - 60 \, x^{13} + 280 \, x^{12} - 330 \, x^{11} - 840 \, x^{10} + 3020 \, x^{9} - 2760 \, x^{8} - 2175 \, x^{7} + 6920 \, x^{6} - 5208 \, x^{5} - 720 \, x^{4} + 3920 \, x^{3} - 2880 \, x^{2} -{\left (x^{14} - 15 \, x^{13} + 53 \, x^{12} + 45 \, x^{11} - 669 \, x^{10} + 1467 \, x^{9} - 505 \, x^{8} - 3009 \, x^{7} + 5440 \, x^{6} - 2888 \, x^{5} - 2208 \, x^{4} + 4400 \, x^{3} - 2944 \, x^{2} + 960 \, x - 128\right )} \sqrt{x + 1} \sqrt{-x + 1} + 960 \, x - 128\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)^(5/2)/(-x + 1)^(17/2),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)**(17/2),x)
[Out]
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GIAC/XCAS [A] time = 0.225481, size = 57, normalized size = 0.56 \[ \frac{{\left (4 \,{\left ({\left (2 \,{\left (x + 1\right )}{\left (x - 14\right )} + 195\right )}{\left (x + 1\right )} - 715\right )}{\left (x + 1\right )} + 6435\right )}{\left (x + 1\right )}^{\frac{7}{2}} \sqrt{-x + 1}}{45045 \,{\left (x - 1\right )}^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)^(5/2)/(-x + 1)^(17/2),x, algorithm="giac")
[Out]