Optimal. Leaf size=101 \[ \frac{8 (x+1)^{5/2}}{15015 (1-x)^{5/2}}+\frac{8 (x+1)^{5/2}}{3003 (1-x)^{7/2}}+\frac{4 (x+1)^{5/2}}{429 (1-x)^{9/2}}+\frac{4 (x+1)^{5/2}}{143 (1-x)^{11/2}}+\frac{(x+1)^{5/2}}{13 (1-x)^{13/2}} \]
[Out]
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Rubi [A] time = 0.0699723, 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 \[ \frac{8 (x+1)^{5/2}}{15015 (1-x)^{5/2}}+\frac{8 (x+1)^{5/2}}{3003 (1-x)^{7/2}}+\frac{4 (x+1)^{5/2}}{429 (1-x)^{9/2}}+\frac{4 (x+1)^{5/2}}{143 (1-x)^{11/2}}+\frac{(x+1)^{5/2}}{13 (1-x)^{13/2}} \]
Antiderivative was successfully verified.
[In] Int[(1 + x)^(3/2)/(1 - x)^(15/2),x]
[Out]
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Rubi in Sympy [A] time = 8.83306, size = 82, normalized size = 0.81 \[ \frac{8 \left (x + 1\right )^{\frac{5}{2}}}{15015 \left (- x + 1\right )^{\frac{5}{2}}} + \frac{8 \left (x + 1\right )^{\frac{5}{2}}}{3003 \left (- x + 1\right )^{\frac{7}{2}}} + \frac{4 \left (x + 1\right )^{\frac{5}{2}}}{429 \left (- x + 1\right )^{\frac{9}{2}}} + \frac{4 \left (x + 1\right )^{\frac{5}{2}}}{143 \left (- x + 1\right )^{\frac{11}{2}}} + \frac{\left (x + 1\right )^{\frac{5}{2}}}{13 \left (- x + 1\right )^{\frac{13}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+x)**(3/2)/(1-x)**(15/2),x)
[Out]
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Mathematica [A] time = 0.0254028, size = 45, normalized size = 0.45 \[ -\frac{(x+1)^2 \sqrt{1-x^2} \left (8 x^4-72 x^3+308 x^2-852 x+1763\right )}{15015 (x-1)^7} \]
Warning: Unable to verify antiderivative.
[In] Integrate[(1 + x)^(3/2)/(1 - x)^(15/2),x]
[Out]
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Maple [A] time = 0.006, size = 35, normalized size = 0.4 \[{\frac{8\,{x}^{4}-72\,{x}^{3}+308\,{x}^{2}-852\,x+1763}{15015} \left ( 1+x \right ) ^{{\frac{5}{2}}} \left ( 1-x \right ) ^{-{\frac{13}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+x)^(3/2)/(1-x)^(15/2),x)
[Out]
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Maxima [A] time = 1.35383, size = 363, normalized size = 3.59 \[ \frac{{\left (-x^{2} + 1\right )}^{\frac{3}{2}}}{5 \,{\left (x^{8} - 8 \, x^{7} + 28 \, x^{6} - 56 \, x^{5} + 70 \, x^{4} - 56 \, x^{3} + 28 \, x^{2} - 8 \, x + 1\right )}} + \frac{6 \, \sqrt{-x^{2} + 1}}{65 \,{\left (x^{7} - 7 \, x^{6} + 21 \, x^{5} - 35 \, x^{4} + 35 \, x^{3} - 21 \, x^{2} + 7 \, x - 1\right )}} + \frac{3 \, \sqrt{-x^{2} + 1}}{715 \,{\left (x^{6} - 6 \, x^{5} + 15 \, x^{4} - 20 \, x^{3} + 15 \, x^{2} - 6 \, x + 1\right )}} - \frac{\sqrt{-x^{2} + 1}}{429 \,{\left (x^{5} - 5 \, x^{4} + 10 \, x^{3} - 10 \, x^{2} + 5 \, x - 1\right )}} + \frac{4 \, \sqrt{-x^{2} + 1}}{3003 \,{\left (x^{4} - 4 \, x^{3} + 6 \, x^{2} - 4 \, x + 1\right )}} - \frac{4 \, \sqrt{-x^{2} + 1}}{5005 \,{\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )}} + \frac{8 \, \sqrt{-x^{2} + 1}}{15015 \,{\left (x^{2} - 2 \, x + 1\right )}} - \frac{8 \, \sqrt{-x^{2} + 1}}{15015 \,{\left (x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)^(3/2)/(-x + 1)^(15/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.20816, size = 365, normalized size = 3.61 \[ \frac{1771 \, x^{13} - 22919 \, x^{12} + 68393 \, x^{11} + 70213 \, x^{10} - 711854 \, x^{9} + 1214070 \, x^{8} + 55770 \, x^{7} - 2594592 \, x^{6} + 2870868 \, x^{5} - 480480 \, x^{4} - 1441440 \, x^{3} + 1921920 \, x^{2} + 13 \,{\left (135 \, x^{12} + 8 \, x^{11} - 6127 \, x^{10} + 24662 \, x^{9} - 25938 \, x^{8} - 50028 \, x^{7} + 162624 \, x^{6} - 137676 \, x^{5} - 36960 \, x^{4} + 147840 \, x^{3} - 147840 \, x^{2} + 73920 \, x\right )} \sqrt{x + 1} \sqrt{-x + 1} - 960960 \, x}{15015 \,{\left (x^{13} - 13 \, x^{12} + 39 \, x^{11} + 39 \, x^{10} - 403 \, x^{9} + 689 \, x^{8} + 13 \, x^{7} - 1443 \, x^{6} + 1742 \, x^{5} - 312 \, x^{4} - 1040 \, x^{3} + 1040 \, x^{2} +{\left (x^{12} - 45 \, x^{10} + 182 \, x^{9} - 193 \, x^{8} - 364 \, x^{7} + 1189 \, x^{6} - 1066 \, x^{5} - 232 \, x^{4} + 1248 \, x^{3} - 1072 \, x^{2} + 416 \, x - 64\right )} \sqrt{x + 1} \sqrt{-x + 1} - 416 \, x + 64\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)^(3/2)/(-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)**(3/2)/(1-x)**(15/2),x)
[Out]
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GIAC/XCAS [A] time = 0.221448, size = 57, normalized size = 0.56 \[ -\frac{{\left (4 \,{\left ({\left (2 \,{\left (x + 1\right )}{\left (x - 12\right )} + 143\right )}{\left (x + 1\right )} - 429\right )}{\left (x + 1\right )} + 3003\right )}{\left (x + 1\right )}^{\frac{5}{2}} \sqrt{-x + 1}}{15015 \,{\left (x - 1\right )}^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)^(3/2)/(-x + 1)^(15/2),x, algorithm="giac")
[Out]