Optimal. Leaf size=38 \[ \frac{3}{5} \left (x^2-4\right )^{5/6}-\frac{24}{\sqrt [6]{x^2-4}}-\frac{48}{7 \left (x^2-4\right )^{7/6}} \]
[Out]
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Rubi [A] time = 0.0377135, antiderivative size = 38, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{3}{5} \left (x^2-4\right )^{5/6}-\frac{24}{\sqrt [6]{x^2-4}}-\frac{48}{7 \left (x^2-4\right )^{7/6}} \]
Antiderivative was successfully verified.
[In] Int[x^5/(-4 + x^2)^(13/6),x]
[Out]
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Rubi in Sympy [A] time = 2.26905, size = 32, normalized size = 0.84 \[ \frac{3 \left (x^{2} - 4\right )^{\frac{5}{6}}}{5} - \frac{24}{\sqrt [6]{x^{2} - 4}} - \frac{48}{7 \left (x^{2} - 4\right )^{\frac{7}{6}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**5/(x**2-4)**(13/6),x)
[Out]
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Mathematica [A] time = 0.0147151, size = 25, normalized size = 0.66 \[ \frac{3 \left (7 x^4-336 x^2+1152\right )}{35 \left (x^2-4\right )^{7/6}} \]
Antiderivative was successfully verified.
[In] Integrate[x^5/(-4 + x^2)^(13/6),x]
[Out]
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Maple [A] time = 0.005, size = 28, normalized size = 0.7 \[{\frac{ \left ( -6+3\,x \right ) \left ( 2+x \right ) \left ( 7\,{x}^{4}-336\,{x}^{2}+1152 \right ) }{35} \left ({x}^{2}-4 \right ) ^{-{\frac{13}{6}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^5/(x^2-4)^(13/6),x)
[Out]
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Maxima [A] time = 1.34152, size = 38, normalized size = 1. \[ \frac{3}{5} \,{\left (x^{2} - 4\right )}^{\frac{5}{6}} - \frac{24}{{\left (x^{2} - 4\right )}^{\frac{1}{6}}} - \frac{48}{7 \,{\left (x^{2} - 4\right )}^{\frac{7}{6}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(x^2 - 4)^(13/6),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.202315, size = 28, normalized size = 0.74 \[ \frac{3 \,{\left (7 \, x^{4} - 336 \, x^{2} + 1152\right )}}{35 \,{\left (x^{2} - 4\right )}^{\frac{7}{6}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(x^2 - 4)^(13/6),x, algorithm="fricas")
[Out]
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Sympy [A] time = 11.7506, size = 82, normalized size = 2.16 \[ \frac{21 x^{4}}{35 x^{2} \sqrt [6]{x^{2} - 4} - 140 \sqrt [6]{x^{2} - 4}} - \frac{1008 x^{2}}{35 x^{2} \sqrt [6]{x^{2} - 4} - 140 \sqrt [6]{x^{2} - 4}} + \frac{3456}{35 x^{2} \sqrt [6]{x^{2} - 4} - 140 \sqrt [6]{x^{2} - 4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**5/(x**2-4)**(13/6),x)
[Out]
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GIAC/XCAS [A] time = 0.200564, size = 35, normalized size = 0.92 \[ \frac{3}{5} \,{\left (x^{2} - 4\right )}^{\frac{5}{6}} - \frac{24 \,{\left (7 \, x^{2} - 26\right )}}{7 \,{\left (x^{2} - 4\right )}^{\frac{7}{6}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(x^2 - 4)^(13/6),x, algorithm="giac")
[Out]