Optimal. Leaf size=38 \[ -\frac{a^3}{x}+a^2 b x^3+\frac{3}{7} a b^2 x^7+\frac{b^3 x^{11}}{11} \]
[Out]
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Rubi [A] time = 0.0359539, antiderivative size = 38, 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 \[ -\frac{a^3}{x}+a^2 b x^3+\frac{3}{7} a b^2 x^7+\frac{b^3 x^{11}}{11} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^4)^3/x^2,x]
[Out]
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Rubi in Sympy [A] time = 6.7243, size = 32, normalized size = 0.84 \[ - \frac{a^{3}}{x} + a^{2} b x^{3} + \frac{3 a b^{2} x^{7}}{7} + \frac{b^{3} x^{11}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**4+a)**3/x**2,x)
[Out]
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Mathematica [A] time = 0.00699419, size = 38, normalized size = 1. \[ -\frac{a^3}{x}+a^2 b x^3+\frac{3}{7} a b^2 x^7+\frac{b^3 x^{11}}{11} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^4)^3/x^2,x]
[Out]
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Maple [A] time = 0.005, size = 35, normalized size = 0.9 \[ -{\frac{{a}^{3}}{x}}+{a}^{2}b{x}^{3}+{\frac{3\,a{b}^{2}{x}^{7}}{7}}+{\frac{{b}^{3}{x}^{11}}{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^4+a)^3/x^2,x)
[Out]
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Maxima [A] time = 1.43845, size = 46, normalized size = 1.21 \[ \frac{1}{11} \, b^{3} x^{11} + \frac{3}{7} \, a b^{2} x^{7} + a^{2} b x^{3} - \frac{a^{3}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^3/x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.219918, size = 50, normalized size = 1.32 \[ \frac{7 \, b^{3} x^{12} + 33 \, a b^{2} x^{8} + 77 \, a^{2} b x^{4} - 77 \, a^{3}}{77 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^3/x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.03662, size = 32, normalized size = 0.84 \[ - \frac{a^{3}}{x} + a^{2} b x^{3} + \frac{3 a b^{2} x^{7}}{7} + \frac{b^{3} x^{11}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**4+a)**3/x**2,x)
[Out]
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GIAC/XCAS [A] time = 0.233754, size = 46, normalized size = 1.21 \[ \frac{1}{11} \, b^{3} x^{11} + \frac{3}{7} \, a b^{2} x^{7} + a^{2} b x^{3} - \frac{a^{3}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^3/x^2,x, algorithm="giac")
[Out]