Optimal. Leaf size=44 \[ -\frac{b^3 \log (a x+b)}{a^4}+\frac{b^2 x}{a^3}-\frac{b x^2}{2 a^2}+\frac{x^3}{3 a} \]
[Out]
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Rubi [A] time = 0.0618754, antiderivative size = 44, 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 \[ -\frac{b^3 \log (a x+b)}{a^4}+\frac{b^2 x}{a^3}-\frac{b x^2}{2 a^2}+\frac{x^3}{3 a} \]
Antiderivative was successfully verified.
[In] Int[x^2/(a + b/x),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ b^{2} \int \frac{1}{a^{3}}\, dx + \frac{x^{3}}{3 a} - \frac{b \int x\, dx}{a^{2}} - \frac{b^{3} \log{\left (a x + b \right )}}{a^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2/(a+b/x),x)
[Out]
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Mathematica [A] time = 0.00632414, size = 44, normalized size = 1. \[ -\frac{b^3 \log (a x+b)}{a^4}+\frac{b^2 x}{a^3}-\frac{b x^2}{2 a^2}+\frac{x^3}{3 a} \]
Antiderivative was successfully verified.
[In] Integrate[x^2/(a + b/x),x]
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Maple [A] time = 0.004, size = 41, normalized size = 0.9 \[{\frac{{b}^{2}x}{{a}^{3}}}-{\frac{b{x}^{2}}{2\,{a}^{2}}}+{\frac{{x}^{3}}{3\,a}}-{\frac{{b}^{3}\ln \left ( ax+b \right ) }{{a}^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2/(a+b/x),x)
[Out]
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Maxima [A] time = 1.43947, size = 57, normalized size = 1.3 \[ -\frac{b^{3} \log \left (a x + b\right )}{a^{4}} + \frac{2 \, a^{2} x^{3} - 3 \, a b x^{2} + 6 \, b^{2} x}{6 \, a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(a + b/x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.22032, size = 55, normalized size = 1.25 \[ \frac{2 \, a^{3} x^{3} - 3 \, a^{2} b x^{2} + 6 \, a b^{2} x - 6 \, b^{3} \log \left (a x + b\right )}{6 \, a^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(a + b/x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.12002, size = 37, normalized size = 0.84 \[ \frac{x^{3}}{3 a} - \frac{b x^{2}}{2 a^{2}} + \frac{b^{2} x}{a^{3}} - \frac{b^{3} \log{\left (a x + b \right )}}{a^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2/(a+b/x),x)
[Out]
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GIAC/XCAS [A] time = 0.223908, size = 58, normalized size = 1.32 \[ -\frac{b^{3}{\rm ln}\left ({\left | a x + b \right |}\right )}{a^{4}} + \frac{2 \, a^{2} x^{3} - 3 \, a b x^{2} + 6 \, b^{2} x}{6 \, a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(a + b/x),x, algorithm="giac")
[Out]