Optimal. Leaf size=22 \[ \frac{\log (x)}{a^3}-\frac{\log \left (a^3+x^3\right )}{3 a^3} \]
[Out]
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Rubi [A] time = 0.0236263, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.308 \[ \frac{\log (x)}{a^3}-\frac{\log \left (a^3+x^3\right )}{3 a^3} \]
Antiderivative was successfully verified.
[In] Int[1/(x*(a^3 + x^3)),x]
[Out]
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Rubi in Sympy [A] time = 2.39399, size = 22, normalized size = 1. \[ \frac{\log{\left (x^{3} \right )}}{3 a^{3}} - \frac{\log{\left (a^{3} + x^{3} \right )}}{3 a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x/(a**3+x**3),x)
[Out]
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Mathematica [A] time = 0.00625151, size = 22, normalized size = 1. \[ \frac{\log (x)}{a^3}-\frac{\log \left (a^3+x^3\right )}{3 a^3} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x*(a^3 + x^3)),x]
[Out]
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Maple [A] time = 0.01, size = 34, normalized size = 1.6 \[ -{\frac{\ln \left ( a+x \right ) }{3\,{a}^{3}}}-{\frac{\ln \left ({a}^{2}-ax+{x}^{2} \right ) }{3\,{a}^{3}}}+{\frac{\ln \left ( x \right ) }{{a}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x/(a^3+x^3),x)
[Out]
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Maxima [A] time = 1.37183, size = 31, normalized size = 1.41 \[ -\frac{\log \left (a^{3} + x^{3}\right )}{3 \, a^{3}} + \frac{\log \left (x^{3}\right )}{3 \, a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a^3 + x^3)*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.2078, size = 24, normalized size = 1.09 \[ -\frac{\log \left (a^{3} + x^{3}\right ) - 3 \, \log \left (x\right )}{3 \, a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a^3 + x^3)*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.254326, size = 19, normalized size = 0.86 \[ \frac{\log{\left (x \right )}}{a^{3}} - \frac{\log{\left (a^{3} + x^{3} \right )}}{3 a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x/(a**3+x**3),x)
[Out]
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GIAC/XCAS [A] time = 0.207743, size = 30, normalized size = 1.36 \[ -\frac{{\rm ln}\left ({\left | a^{3} + x^{3} \right |}\right )}{3 \, a^{3}} + \frac{{\rm ln}\left ({\left | x \right |}\right )}{a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a^3 + x^3)*x),x, algorithm="giac")
[Out]