Optimal. Leaf size=23 \[ a^2 x-\frac{2 a b}{x}-\frac{b^2}{3 x^3} \]
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Rubi [A] time = 0.0334907, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ a^2 x-\frac{2 a b}{x}-\frac{b^2}{3 x^3} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x^2)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{2 a b}{x} - \frac{b^{2}}{3 x^{3}} + \int a^{2}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x**2)**2,x)
[Out]
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Mathematica [A] time = 0.00878449, size = 23, normalized size = 1. \[ a^2 x-\frac{2 a b}{x}-\frac{b^2}{3 x^3} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x^2)^2,x]
[Out]
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Maple [A] time = 0.008, size = 22, normalized size = 1. \[ -{\frac{{b}^{2}}{3\,{x}^{3}}}-2\,{\frac{ab}{x}}+x{a}^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x^2)^2,x)
[Out]
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Maxima [A] time = 1.43518, size = 28, normalized size = 1.22 \[ a^{2} x - \frac{2 \, a b}{x} - \frac{b^{2}}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212713, size = 35, normalized size = 1.52 \[ \frac{3 \, a^{2} x^{4} - 6 \, a b x^{2} - b^{2}}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.17635, size = 20, normalized size = 0.87 \[ a^{2} x - \frac{6 a b x^{2} + b^{2}}{3 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x**2)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.227513, size = 30, normalized size = 1.3 \[ a^{2} x - \frac{6 \, a b x^{2} + b^{2}}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^2,x, algorithm="giac")
[Out]