Optimal. Leaf size=16 \[ \frac{1}{3 b \left (a+\frac{b}{x^3}\right )} \]
[Out]
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Rubi [A] time = 0.018871, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{1}{3 b \left (a+\frac{b}{x^3}\right )} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b/x^3)^2*x^4),x]
[Out]
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Rubi in Sympy [A] time = 2.1281, size = 10, normalized size = 0.62 \[ \frac{1}{3 b \left (a + \frac{b}{x^{3}}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x**3)**2/x**4,x)
[Out]
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Mathematica [A] time = 0.0087141, size = 16, normalized size = 1. \[ -\frac{1}{3 a \left (a x^3+b\right )} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b/x^3)^2*x^4),x]
[Out]
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Maple [A] time = 0.002, size = 15, normalized size = 0.9 \[ -{\frac{1}{ \left ( 3\,a{x}^{3}+3\,b \right ) a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x^3)^2/x^4,x)
[Out]
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Maxima [A] time = 1.43496, size = 19, normalized size = 1.19 \[ \frac{1}{3 \,{\left (a + \frac{b}{x^{3}}\right )} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^3)^2*x^4),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.221356, size = 20, normalized size = 1.25 \[ -\frac{1}{3 \,{\left (a^{2} x^{3} + a b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^3)^2*x^4),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.38853, size = 15, normalized size = 0.94 \[ - \frac{1}{3 a^{2} x^{3} + 3 a b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b/x**3)**2/x**4,x)
[Out]
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GIAC/XCAS [A] time = 0.233998, size = 19, normalized size = 1.19 \[ -\frac{1}{3 \,{\left (a x^{3} + b\right )} a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^3)^2*x^4),x, algorithm="giac")
[Out]