Optimal. Leaf size=19 \[ -\frac{\left (a+b \sqrt [3]{x}\right )^3}{a x} \]
[Out]
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Rubi [A] time = 0.0162551, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ -\frac{\left (a+b \sqrt [3]{x}\right )^3}{a x} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^(1/3))^2/x^2,x]
[Out]
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Rubi in Sympy [A] time = 2.85974, size = 14, normalized size = 0.74 \[ - \frac{\left (a + b \sqrt [3]{x}\right )^{3}}{a x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/3))**2/x**2,x)
[Out]
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Mathematica [A] time = 0.0149112, size = 28, normalized size = 1.47 \[ -\frac{a^2}{x}-\frac{3 a b}{x^{2/3}}-\frac{3 b^2}{\sqrt [3]{x}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^(1/3))^2/x^2,x]
[Out]
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Maple [A] time = 0.008, size = 25, normalized size = 1.3 \[ -{\frac{{a}^{2}}{x}}-3\,{\frac{ab}{{x}^{2/3}}}-3\,{\frac{{b}^{2}}{\sqrt [3]{x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/3))^2/x^2,x)
[Out]
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Maxima [A] time = 1.47163, size = 32, normalized size = 1.68 \[ -\frac{3 \, b^{2} x^{\frac{2}{3}} + 3 \, a b x^{\frac{1}{3}} + a^{2}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^2/x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.21334, size = 32, normalized size = 1.68 \[ -\frac{3 \, b^{2} x^{\frac{2}{3}} + 3 \, a b x^{\frac{1}{3}} + a^{2}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^2/x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.14483, size = 26, normalized size = 1.37 \[ - \frac{a^{2}}{x} - \frac{3 a b}{x^{\frac{2}{3}}} - \frac{3 b^{2}}{\sqrt [3]{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/3))**2/x**2,x)
[Out]
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GIAC/XCAS [A] time = 0.260883, size = 32, normalized size = 1.68 \[ -\frac{3 \, b^{2} x^{\frac{2}{3}} + 3 \, a b x^{\frac{1}{3}} + a^{2}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^2/x^2,x, algorithm="giac")
[Out]