Optimal. Leaf size=17 \[ \frac{1}{8 b \left (a-b x^2\right )^4} \]
[Out]
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Rubi [A] time = 0.0112372, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083 \[ \frac{1}{8 b \left (a-b x^2\right )^4} \]
Antiderivative was successfully verified.
[In] Int[x/(a - b*x^2)^5,x]
[Out]
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Rubi in Sympy [A] time = 2.68558, size = 12, normalized size = 0.71 \[ \frac{1}{8 b \left (a - b x^{2}\right )^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(-b*x**2+a)**5,x)
[Out]
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Mathematica [A] time = 0.00765399, size = 17, normalized size = 1. \[ \frac{1}{8 b \left (a-b x^2\right )^4} \]
Antiderivative was successfully verified.
[In] Integrate[x/(a - b*x^2)^5,x]
[Out]
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Maple [A] time = 0.001, size = 17, normalized size = 1. \[{\frac{1}{8\,b \left ( b{x}^{2}-a \right ) ^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(-b*x^2+a)^5,x)
[Out]
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Maxima [A] time = 1.34582, size = 22, normalized size = 1.29 \[ \frac{1}{8 \,{\left (b x^{2} - a\right )}^{4} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-x/(b*x^2 - a)^5,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.221801, size = 65, normalized size = 3.82 \[ \frac{1}{8 \,{\left (b^{5} x^{8} - 4 \, a b^{4} x^{6} + 6 \, a^{2} b^{3} x^{4} - 4 \, a^{3} b^{2} x^{2} + a^{4} b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-x/(b*x^2 - a)^5,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.69979, size = 49, normalized size = 2.88 \[ \frac{1}{8 a^{4} b - 32 a^{3} b^{2} x^{2} + 48 a^{2} b^{3} x^{4} - 32 a b^{4} x^{6} + 8 b^{5} x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(-b*x**2+a)**5,x)
[Out]
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GIAC/XCAS [A] time = 0.211518, size = 22, normalized size = 1.29 \[ \frac{1}{8 \,{\left (b x^{2} - a\right )}^{4} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-x/(b*x^2 - a)^5,x, algorithm="giac")
[Out]