Optimal. Leaf size=14 \[ \frac{(a x+b)^3}{3 a} \]
[Out]
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Rubi [A] time = 0.0164609, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{(a x+b)^3}{3 a} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^2*x^2,x]
[Out]
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Rubi in Sympy [A] time = 2.96425, size = 8, normalized size = 0.57 \[ \frac{\left (a x + b\right )^{3}}{3 a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**2*x**2,x)
[Out]
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Mathematica [A] time = 0.00283409, size = 14, normalized size = 1. \[ \frac{(a x+b)^3}{3 a} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^2*x^2,x]
[Out]
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Maple [A] time = 0.001, size = 13, normalized size = 0.9 \[{\frac{ \left ( ax+b \right ) ^{3}}{3\,a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^2*x^2,x)
[Out]
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Maxima [A] time = 1.446, size = 27, normalized size = 1.93 \[ \frac{1}{3} \, a^{2} x^{3} + a b x^{2} + b^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^2*x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.217358, size = 27, normalized size = 1.93 \[ \frac{1}{3} \, a^{2} x^{3} + a b x^{2} + b^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^2*x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.085349, size = 19, normalized size = 1.36 \[ \frac{a^{2} x^{3}}{3} + a b x^{2} + b^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**2*x**2,x)
[Out]
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GIAC/XCAS [A] time = 0.222092, size = 27, normalized size = 1.93 \[ \frac{1}{3} \, a^{2} x^{3} + a b x^{2} + b^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^2*x^2,x, algorithm="giac")
[Out]