Optimal. Leaf size=46 \[ -\frac{b^2}{3 a^3 \left (a x^3+b\right )}-\frac{2 b \log \left (a x^3+b\right )}{3 a^3}+\frac{x^3}{3 a^2} \]
[Out]
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Rubi [A] time = 0.0934779, antiderivative size = 46, 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 \[ -\frac{b^2}{3 a^3 \left (a x^3+b\right )}-\frac{2 b \log \left (a x^3+b\right )}{3 a^3}+\frac{x^3}{3 a^2} \]
Antiderivative was successfully verified.
[In] Int[x^2/(a + b/x^3)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{\int ^{x^{3}} \frac{1}{a^{2}}\, dx}{3} - \frac{b^{2}}{3 a^{3} \left (a x^{3} + b\right )} - \frac{2 b \log{\left (a x^{3} + b \right )}}{3 a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2/(a+b/x**3)**2,x)
[Out]
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Mathematica [A] time = 0.0281812, size = 38, normalized size = 0.83 \[ \frac{-\frac{b^2}{a x^3+b}-2 b \log \left (a x^3+b\right )+a x^3}{3 a^3} \]
Antiderivative was successfully verified.
[In] Integrate[x^2/(a + b/x^3)^2,x]
[Out]
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Maple [A] time = 0.008, size = 41, normalized size = 0.9 \[{\frac{{x}^{3}}{3\,{a}^{2}}}-{\frac{{b}^{2}}{3\,{a}^{3} \left ( a{x}^{3}+b \right ) }}-{\frac{2\,b\ln \left ( a{x}^{3}+b \right ) }{3\,{a}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2/(a+b/x^3)^2,x)
[Out]
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Maxima [A] time = 1.4272, size = 58, normalized size = 1.26 \[ -\frac{b^{2}}{3 \,{\left (a^{4} x^{3} + a^{3} b\right )}} + \frac{x^{3}}{3 \, a^{2}} - \frac{2 \, b \log \left (a x^{3} + b\right )}{3 \, a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(a + b/x^3)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.232567, size = 76, normalized size = 1.65 \[ \frac{a^{2} x^{6} + a b x^{3} - b^{2} - 2 \,{\left (a b x^{3} + b^{2}\right )} \log \left (a x^{3} + b\right )}{3 \,{\left (a^{4} x^{3} + a^{3} b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(a + b/x^3)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.74545, size = 42, normalized size = 0.91 \[ - \frac{b^{2}}{3 a^{4} x^{3} + 3 a^{3} b} + \frac{x^{3}}{3 a^{2}} - \frac{2 b \log{\left (a x^{3} + b \right )}}{3 a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2/(a+b/x**3)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.22986, size = 55, normalized size = 1.2 \[ \frac{x^{3}}{3 \, a^{2}} - \frac{2 \, b{\rm ln}\left ({\left | a x^{3} + b \right |}\right )}{3 \, a^{3}} - \frac{b^{2}}{3 \,{\left (a x^{3} + b\right )} a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(a + b/x^3)^2,x, algorithm="giac")
[Out]