Optimal. Leaf size=39 \[ -\frac{a^3}{2 x^2}+3 a^2 b x+\frac{3}{4} a b^2 x^4+\frac{b^3 x^7}{7} \]
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Rubi [A] time = 0.0377036, antiderivative size = 39, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{a^3}{2 x^2}+3 a^2 b x+\frac{3}{4} a b^2 x^4+\frac{b^3 x^7}{7} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^3/x^3,x]
[Out]
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Rubi in Sympy [A] time = 6.634, size = 36, normalized size = 0.92 \[ - \frac{a^{3}}{2 x^{2}} + 3 a^{2} b x + \frac{3 a b^{2} x^{4}}{4} + \frac{b^{3} x^{7}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**3/x**3,x)
[Out]
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Mathematica [A] time = 0.0115453, size = 39, normalized size = 1. \[ -\frac{a^3}{2 x^2}+3 a^2 b x+\frac{3}{4} a b^2 x^4+\frac{b^3 x^7}{7} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^3/x^3,x]
[Out]
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Maple [A] time = 0.005, size = 34, normalized size = 0.9 \[ -{\frac{{a}^{3}}{2\,{x}^{2}}}+3\,{a}^{2}bx+{\frac{3\,a{b}^{2}{x}^{4}}{4}}+{\frac{{b}^{3}{x}^{7}}{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^3/x^3,x)
[Out]
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Maxima [A] time = 1.42231, size = 45, normalized size = 1.15 \[ \frac{1}{7} \, b^{3} x^{7} + \frac{3}{4} \, a b^{2} x^{4} + 3 \, a^{2} b x - \frac{a^{3}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^3/x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.224288, size = 50, normalized size = 1.28 \[ \frac{4 \, b^{3} x^{9} + 21 \, a b^{2} x^{6} + 84 \, a^{2} b x^{3} - 14 \, a^{3}}{28 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^3/x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.08596, size = 36, normalized size = 0.92 \[ - \frac{a^{3}}{2 x^{2}} + 3 a^{2} b x + \frac{3 a b^{2} x^{4}}{4} + \frac{b^{3} x^{7}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**3/x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.212582, size = 45, normalized size = 1.15 \[ \frac{1}{7} \, b^{3} x^{7} + \frac{3}{4} \, a b^{2} x^{4} + 3 \, a^{2} b x - \frac{a^{3}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^3/x^3,x, algorithm="giac")
[Out]