Optimal. Leaf size=23 \[ \frac{a^2 x^4}{4}+a b x^2+b^2 \log (x) \]
[Out]
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Rubi [A] time = 0.0457592, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ \frac{a^2 x^4}{4}+a b x^2+b^2 \log (x) \]
Antiderivative was successfully verified.
[In] Int[(a + b/x^2)^2*x^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{a^{2} \int ^{x^{2}} x\, dx}{2} + a b x^{2} + \frac{b^{2} \log{\left (x^{2} \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x**2)**2*x**3,x)
[Out]
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Mathematica [A] time = 0.00210901, size = 23, normalized size = 1. \[ \frac{a^2 x^4}{4}+a b x^2+b^2 \log (x) \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x^2)^2*x^3,x]
[Out]
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Maple [A] time = 0.003, size = 22, normalized size = 1. \[ ab{x}^{2}+{\frac{{x}^{4}{a}^{2}}{4}}+{b}^{2}\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x^2)^2*x^3,x)
[Out]
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Maxima [A] time = 1.44281, size = 32, normalized size = 1.39 \[ \frac{1}{4} \, a^{2} x^{4} + a b x^{2} + \frac{1}{2} \, b^{2} \log \left (x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^2*x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.231294, size = 28, normalized size = 1.22 \[ \frac{1}{4} \, a^{2} x^{4} + a b x^{2} + b^{2} \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^2*x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.07473, size = 20, normalized size = 0.87 \[ \frac{a^{2} x^{4}}{4} + a b x^{2} + b^{2} \log{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x**2)**2*x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.228774, size = 30, normalized size = 1.3 \[ \frac{1}{4} \, a^{2} x^{4} + a b x^{2} + b^{2}{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^2*x^3,x, algorithm="giac")
[Out]