Optimal. Leaf size=19 \[ \frac{x^{16}}{16 b \left (a x^8+b\right )^2} \]
[Out]
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Rubi [A] time = 0.017464, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{x^{16}}{16 b \left (a x^8+b\right )^2} \]
Antiderivative was successfully verified.
[In] Int[(b/x^5 + a*x^3)^(-3),x]
[Out]
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Rubi in Sympy [A] time = 3.29014, size = 14, normalized size = 0.74 \[ \frac{x^{16}}{16 b \left (a x^{8} + b\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b/x**5+a*x**3)**3,x)
[Out]
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Mathematica [A] time = 0.0170535, size = 24, normalized size = 1.26 \[ -\frac{2 a x^8+b}{16 a^2 \left (a x^8+b\right )^2} \]
Antiderivative was successfully verified.
[In] Integrate[(b/x^5 + a*x^3)^(-3),x]
[Out]
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Maple [A] time = 0.013, size = 31, normalized size = 1.6 \[ -{\frac{1}{ \left ( 8\,a{x}^{8}+8\,b \right ){a}^{2}}}+{\frac{b}{16\,{a}^{2} \left ( a{x}^{8}+b \right ) ^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b/x^5+a*x^3)^3,x)
[Out]
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Maxima [A] time = 1.37092, size = 49, normalized size = 2.58 \[ -\frac{2 \, a x^{8} + b}{16 \,{\left (a^{4} x^{16} + 2 \, a^{3} b x^{8} + a^{2} b^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a*x^3 + b/x^5)^(-3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.205732, size = 49, normalized size = 2.58 \[ -\frac{2 \, a x^{8} + b}{16 \,{\left (a^{4} x^{16} + 2 \, a^{3} b x^{8} + a^{2} b^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a*x^3 + b/x^5)^(-3),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/(b/x**5+a*x**3)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.215441, size = 30, normalized size = 1.58 \[ -\frac{2 \, a x^{8} + b}{16 \,{\left (a x^{8} + b\right )}^{2} a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a*x^3 + b/x^5)^(-3),x, algorithm="giac")
[Out]