Optimal. Leaf size=30 \[ \frac{a^2 x^6}{6}+\frac{2}{5} a b x^5+\frac{b^2 x^4}{4} \]
[Out]
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Rubi [A] time = 0.0476112, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{a^2 x^6}{6}+\frac{2}{5} a b x^5+\frac{b^2 x^4}{4} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^2*x^5,x]
[Out]
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Rubi in Sympy [A] time = 7.01771, size = 26, normalized size = 0.87 \[ \frac{a^{2} x^{6}}{6} + \frac{2 a b x^{5}}{5} + \frac{b^{2} x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**2*x**5,x)
[Out]
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Mathematica [A] time = 0.00304752, size = 30, normalized size = 1. \[ \frac{a^2 x^6}{6}+\frac{2}{5} a b x^5+\frac{b^2 x^4}{4} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^2*x^5,x]
[Out]
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Maple [A] time = 0.001, size = 25, normalized size = 0.8 \[{\frac{{b}^{2}{x}^{4}}{4}}+{\frac{2\,{x}^{5}ab}{5}}+{\frac{{a}^{2}{x}^{6}}{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^2*x^5,x)
[Out]
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Maxima [A] time = 1.44145, size = 32, normalized size = 1.07 \[ \frac{1}{6} \, a^{2} x^{6} + \frac{2}{5} \, a b x^{5} + \frac{1}{4} \, b^{2} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^2*x^5,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.217434, size = 32, normalized size = 1.07 \[ \frac{1}{6} \, a^{2} x^{6} + \frac{2}{5} \, a b x^{5} + \frac{1}{4} \, b^{2} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^2*x^5,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.091553, size = 26, normalized size = 0.87 \[ \frac{a^{2} x^{6}}{6} + \frac{2 a b x^{5}}{5} + \frac{b^{2} x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**2*x**5,x)
[Out]
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GIAC/XCAS [A] time = 0.222451, size = 32, normalized size = 1.07 \[ \frac{1}{6} \, a^{2} x^{6} + \frac{2}{5} \, a b x^{5} + \frac{1}{4} \, b^{2} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^2*x^5,x, algorithm="giac")
[Out]