Optimal. Leaf size=101 \[ \frac{8 (x+1)^{3/2}}{3465 (1-x)^{3/2}}+\frac{8 (x+1)^{3/2}}{1155 (1-x)^{5/2}}+\frac{4 (x+1)^{3/2}}{231 (1-x)^{7/2}}+\frac{4 (x+1)^{3/2}}{99 (1-x)^{9/2}}+\frac{(x+1)^{3/2}}{11 (1-x)^{11/2}} \]
[Out]
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Rubi [A] time = 0.0685068, 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 \[ \frac{8 (x+1)^{3/2}}{3465 (1-x)^{3/2}}+\frac{8 (x+1)^{3/2}}{1155 (1-x)^{5/2}}+\frac{4 (x+1)^{3/2}}{231 (1-x)^{7/2}}+\frac{4 (x+1)^{3/2}}{99 (1-x)^{9/2}}+\frac{(x+1)^{3/2}}{11 (1-x)^{11/2}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[1 + x]/(1 - x)^(13/2),x]
[Out]
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Rubi in Sympy [A] time = 9.43438, size = 82, normalized size = 0.81 \[ \frac{8 \left (x + 1\right )^{\frac{3}{2}}}{3465 \left (- x + 1\right )^{\frac{3}{2}}} + \frac{8 \left (x + 1\right )^{\frac{3}{2}}}{1155 \left (- x + 1\right )^{\frac{5}{2}}} + \frac{4 \left (x + 1\right )^{\frac{3}{2}}}{231 \left (- x + 1\right )^{\frac{7}{2}}} + \frac{4 \left (x + 1\right )^{\frac{3}{2}}}{99 \left (- x + 1\right )^{\frac{9}{2}}} + \frac{\left (x + 1\right )^{\frac{3}{2}}}{11 \left (- x + 1\right )^{\frac{11}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+x)**(1/2)/(1-x)**(13/2),x)
[Out]
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Mathematica [A] time = 0.0218158, size = 45, normalized size = 0.45 \[ \frac{\sqrt{1-x^2} \left (8 x^5-48 x^4+124 x^3-184 x^2+183 x+547\right )}{3465 (x-1)^6} \]
Warning: Unable to verify antiderivative.
[In] Integrate[Sqrt[1 + x]/(1 - x)^(13/2),x]
[Out]
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Maple [A] time = 0.005, size = 35, normalized size = 0.4 \[{\frac{8\,{x}^{4}-56\,{x}^{3}+180\,{x}^{2}-364\,x+547}{3465} \left ( 1+x \right ) ^{{\frac{3}{2}}} \left ( 1-x \right ) ^{-{\frac{11}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+x)^(1/2)/(1-x)^(13/2),x)
[Out]
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Maxima [A] time = 1.35381, size = 232, normalized size = 2.3 \[ \frac{2 \, \sqrt{-x^{2} + 1}}{11 \,{\left (x^{6} - 6 \, x^{5} + 15 \, x^{4} - 20 \, x^{3} + 15 \, x^{2} - 6 \, x + 1\right )}} + \frac{\sqrt{-x^{2} + 1}}{99 \,{\left (x^{5} - 5 \, x^{4} + 10 \, x^{3} - 10 \, x^{2} + 5 \, x - 1\right )}} - \frac{4 \, \sqrt{-x^{2} + 1}}{693 \,{\left (x^{4} - 4 \, x^{3} + 6 \, x^{2} - 4 \, x + 1\right )}} + \frac{4 \, \sqrt{-x^{2} + 1}}{1155 \,{\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )}} - \frac{8 \, \sqrt{-x^{2} + 1}}{3465 \,{\left (x^{2} - 2 \, x + 1\right )}} + \frac{8 \, \sqrt{-x^{2} + 1}}{3465 \,{\left (x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x + 1)/(-x + 1)^(13/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.210389, size = 312, normalized size = 3.09 \[ \frac{555 \, x^{11} - 88 \, x^{10} - 17831 \, x^{9} + 60390 \, x^{8} - 43824 \, x^{7} - 117348 \, x^{6} + 255486 \, x^{5} - 147840 \, x^{4} - 101640 \, x^{3} + 221760 \, x^{2} - 11 \,{\left (49 \, x^{10} - 547 \, x^{9} + 1416 \, x^{8} + 1014 \, x^{7} - 9828 \, x^{6} + 14826 \, x^{5} - 3360 \, x^{4} - 14280 \, x^{3} + 20160 \, x^{2} - 10080 \, x\right )} \sqrt{x + 1} \sqrt{-x + 1} - 110880 \, x}{3465 \,{\left (x^{11} - 33 \, x^{9} + 110 \, x^{8} - 77 \, x^{7} - 220 \, x^{6} + 473 \, x^{5} - 242 \, x^{4} - 220 \, x^{3} + 352 \, x^{2} -{\left (x^{10} - 11 \, x^{9} + 28 \, x^{8} + 22 \, x^{7} - 199 \, x^{6} + 297 \, x^{5} - 54 \, x^{4} - 308 \, x^{3} + 368 \, x^{2} - 176 \, x + 32\right )} \sqrt{x + 1} \sqrt{-x + 1} - 176 \, x + 32\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x + 1)/(-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)**(1/2)/(1-x)**(13/2),x)
[Out]
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GIAC/XCAS [A] time = 0.2173, size = 57, normalized size = 0.56 \[ \frac{{\left (4 \,{\left ({\left (2 \,{\left (x + 1\right )}{\left (x - 10\right )} + 99\right )}{\left (x + 1\right )} - 231\right )}{\left (x + 1\right )} + 1155\right )}{\left (x + 1\right )}^{\frac{3}{2}} \sqrt{-x + 1}}{3465 \,{\left (x - 1\right )}^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x + 1)/(-x + 1)^(13/2),x, algorithm="giac")
[Out]