Optimal. Leaf size=19 \[ -\frac{\left (a+b x^3\right )^4}{12 a x^{12}} \]
[Out]
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Rubi [A] time = 0.0160891, antiderivative size = 19, 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 \[ -\frac{\left (a+b x^3\right )^4}{12 a x^{12}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^3/x^13,x]
[Out]
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Rubi in Sympy [A] time = 2.75094, size = 15, normalized size = 0.79 \[ - \frac{\left (a + b x^{3}\right )^{4}}{12 a x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**3/x**13,x)
[Out]
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Mathematica [B] time = 0.00630495, size = 43, normalized size = 2.26 \[ -\frac{a^3}{12 x^{12}}-\frac{a^2 b}{3 x^9}-\frac{a b^2}{2 x^6}-\frac{b^3}{3 x^3} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^3/x^13,x]
[Out]
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Maple [B] time = 0.008, size = 36, normalized size = 1.9 \[ -{\frac{{a}^{3}}{12\,{x}^{12}}}-{\frac{a{b}^{2}}{2\,{x}^{6}}}-{\frac{{a}^{2}b}{3\,{x}^{9}}}-{\frac{{b}^{3}}{3\,{x}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^3/x^13,x)
[Out]
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Maxima [A] time = 1.44204, size = 47, normalized size = 2.47 \[ -\frac{4 \, b^{3} x^{9} + 6 \, a b^{2} x^{6} + 4 \, a^{2} b x^{3} + a^{3}}{12 \, x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^3/x^13,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.222255, size = 47, normalized size = 2.47 \[ -\frac{4 \, b^{3} x^{9} + 6 \, a b^{2} x^{6} + 4 \, a^{2} b x^{3} + a^{3}}{12 \, x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^3/x^13,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.82933, size = 37, normalized size = 1.95 \[ - \frac{a^{3} + 4 a^{2} b x^{3} + 6 a b^{2} x^{6} + 4 b^{3} x^{9}}{12 x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**3/x**13,x)
[Out]
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GIAC/XCAS [A] time = 0.216427, size = 47, normalized size = 2.47 \[ -\frac{4 \, b^{3} x^{9} + 6 \, a b^{2} x^{6} + 4 \, a^{2} b x^{3} + a^{3}}{12 \, x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^3/x^13,x, algorithm="giac")
[Out]