Optimal. Leaf size=61 \[ \frac{2 (x+1)^{7/2}}{693 (1-x)^{7/2}}+\frac{2 (x+1)^{7/2}}{99 (1-x)^{9/2}}+\frac{(x+1)^{7/2}}{11 (1-x)^{11/2}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0376054, antiderivative size = 61, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ \frac{2 (x+1)^{7/2}}{693 (1-x)^{7/2}}+\frac{2 (x+1)^{7/2}}{99 (1-x)^{9/2}}+\frac{(x+1)^{7/2}}{11 (1-x)^{11/2}} \]
Antiderivative was successfully verified.
[In] Int[(1 + x)^(5/2)/(1 - x)^(13/2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 5.26874, size = 48, normalized size = 0.79 \[ \frac{2 \left (x + 1\right )^{\frac{7}{2}}}{693 \left (- x + 1\right )^{\frac{7}{2}}} + \frac{2 \left (x + 1\right )^{\frac{7}{2}}}{99 \left (- x + 1\right )^{\frac{9}{2}}} + \frac{\left (x + 1\right )^{\frac{7}{2}}}{11 \left (- x + 1\right )^{\frac{11}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+x)**(5/2)/(1-x)**(13/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0230263, size = 35, normalized size = 0.57 \[ \frac{(x+1)^3 \sqrt{1-x^2} \left (2 x^2-18 x+79\right )}{693 (x-1)^6} \]
Warning: Unable to verify antiderivative.
[In] Integrate[(1 + x)^(5/2)/(1 - x)^(13/2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.003, size = 25, normalized size = 0.4 \[{\frac{2\,{x}^{2}-18\,x+79}{693} \left ( 1+x \right ) ^{{\frac{7}{2}}} \left ( 1-x \right ) ^{-{\frac{11}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+x)^(5/2)/(1-x)^(13/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.34855, size = 363, normalized size = 5.95 \[ \frac{{\left (-x^{2} + 1\right )}^{\frac{5}{2}}}{3 \,{\left (x^{8} - 8 \, x^{7} + 28 \, x^{6} - 56 \, x^{5} + 70 \, x^{4} - 56 \, x^{3} + 28 \, x^{2} - 8 \, x + 1\right )}} + \frac{5 \,{\left (-x^{2} + 1\right )}^{\frac{3}{2}}}{12 \,{\left (x^{7} - 7 \, x^{6} + 21 \, x^{5} - 35 \, x^{4} + 35 \, x^{3} - 21 \, x^{2} + 7 \, x - 1\right )}} + \frac{5 \, \sqrt{-x^{2} + 1}}{22 \,{\left (x^{6} - 6 \, x^{5} + 15 \, x^{4} - 20 \, x^{3} + 15 \, x^{2} - 6 \, x + 1\right )}} + \frac{5 \, \sqrt{-x^{2} + 1}}{396 \,{\left (x^{5} - 5 \, x^{4} + 10 \, x^{3} - 10 \, x^{2} + 5 \, x - 1\right )}} - \frac{5 \, \sqrt{-x^{2} + 1}}{693 \,{\left (x^{4} - 4 \, x^{3} + 6 \, x^{2} - 4 \, x + 1\right )}} + \frac{\sqrt{-x^{2} + 1}}{231 \,{\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )}} - \frac{2 \, \sqrt{-x^{2} + 1}}{693 \,{\left (x^{2} - 2 \, x + 1\right )}} + \frac{2 \, \sqrt{-x^{2} + 1}}{693 \,{\left (x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)^(5/2)/(-x + 1)^(13/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.207694, size = 312, normalized size = 5.11 \[ \frac{81 \, x^{11} - 22 \, x^{10} - 2552 \, x^{9} + 8976 \, x^{8} - 7491 \, x^{7} - 21714 \, x^{6} + 38346 \, x^{5} - 7392 \, x^{4} - 9240 \, x^{3} + 22176 \, x^{2} - 11 \,{\left (7 \, x^{10} - 79 \, x^{9} + 207 \, x^{8} + 117 \, x^{7} - 1554 \, x^{6} + 2310 \, x^{5} + 336 \, x^{4} - 1848 \, x^{3} + 2016 \, x^{2} - 2016 \, x\right )} \sqrt{x + 1} \sqrt{-x + 1} - 22176 \, x}{693 \,{\left (x^{11} - 33 \, x^{9} + 110 \, x^{8} - 77 \, x^{7} - 220 \, x^{6} + 473 \, x^{5} - 242 \, x^{4} - 220 \, x^{3} + 352 \, x^{2} -{\left (x^{10} - 11 \, x^{9} + 28 \, x^{8} + 22 \, x^{7} - 199 \, x^{6} + 297 \, x^{5} - 54 \, x^{4} - 308 \, x^{3} + 368 \, x^{2} - 176 \, x + 32\right )} \sqrt{x + 1} \sqrt{-x + 1} - 176 \, x + 32\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)^(5/2)/(-x + 1)^(13/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
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)**(13/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.219973, size = 39, normalized size = 0.64 \[ \frac{{\left (2 \,{\left (x + 1\right )}{\left (x - 10\right )} + 99\right )}{\left (x + 1\right )}^{\frac{7}{2}} \sqrt{-x + 1}}{693 \,{\left (x - 1\right )}^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)^(5/2)/(-x + 1)^(13/2),x, algorithm="giac")
[Out]