Optimal. Leaf size=23 \[ -\frac{a^2}{5 x^5}-\frac{a b}{x^2}+b^2 x \]
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Rubi [A] time = 0.0280289, antiderivative size = 23, 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 \[ -\frac{a^2}{5 x^5}-\frac{a b}{x^2}+b^2 x \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^2/x^6,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{2}}{5 x^{5}} - \frac{a b}{x^{2}} + \int b^{2}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**2/x**6,x)
[Out]
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Mathematica [A] time = 0.00125369, size = 23, normalized size = 1. \[ -\frac{a^2}{5 x^5}-\frac{a b}{x^2}+b^2 x \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^2/x^6,x]
[Out]
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Maple [A] time = 0.007, size = 22, normalized size = 1. \[ -{\frac{{a}^{2}}{5\,{x}^{5}}}-{\frac{ab}{{x}^{2}}}+{b}^{2}x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^2/x^6,x)
[Out]
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Maxima [A] time = 1.44031, size = 30, normalized size = 1.3 \[ b^{2} x - \frac{5 \, a b x^{3} + a^{2}}{5 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^2/x^6,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.256298, size = 35, normalized size = 1.52 \[ \frac{5 \, b^{2} x^{6} - 5 \, a b x^{3} - a^{2}}{5 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^2/x^6,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.30997, size = 20, normalized size = 0.87 \[ b^{2} x - \frac{a^{2} + 5 a b x^{3}}{5 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**2/x**6,x)
[Out]
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GIAC/XCAS [A] time = 0.243837, size = 30, normalized size = 1.3 \[ b^{2} x - \frac{5 \, a b x^{3} + a^{2}}{5 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^2/x^6,x, algorithm="giac")
[Out]