Optimal. Leaf size=24 \[ \frac{\log (x)}{a^4}-\frac{\log \left (a^4-x^4\right )}{4 a^4} \]
[Out]
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Rubi [A] time = 0.0272014, antiderivative size = 24, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.267 \[ \frac{\log (x)}{a^4}-\frac{\log \left (a^4-x^4\right )}{4 a^4} \]
Antiderivative was successfully verified.
[In] Int[1/(x*(a^4 - x^4)),x]
[Out]
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Rubi in Sympy [A] time = 2.59572, size = 22, normalized size = 0.92 \[ \frac{\log{\left (x^{4} \right )}}{4 a^{4}} - \frac{\log{\left (a^{4} - x^{4} \right )}}{4 a^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x/(a**4-x**4),x)
[Out]
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Mathematica [A] time = 0.00884881, size = 24, normalized size = 1. \[ \frac{\log (x)}{a^4}-\frac{\log \left (x^4-a^4\right )}{4 a^4} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x*(a^4 - x^4)),x]
[Out]
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Maple [A] time = 0.01, size = 41, normalized size = 1.7 \[ -{\frac{\ln \left ( a+x \right ) }{4\,{a}^{4}}}+{\frac{\ln \left ( x \right ) }{{a}^{4}}}-{\frac{\ln \left ({a}^{2}+{x}^{2} \right ) }{4\,{a}^{4}}}-{\frac{\ln \left ( -a+x \right ) }{4\,{a}^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x/(a^4-x^4),x)
[Out]
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Maxima [A] time = 1.35116, size = 34, normalized size = 1.42 \[ -\frac{\log \left (-a^{4} + x^{4}\right )}{4 \, a^{4}} + \frac{\log \left (x^{4}\right )}{4 \, a^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a^4 - x^4)*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.198396, size = 27, normalized size = 1.12 \[ -\frac{\log \left (-a^{4} + x^{4}\right ) - 4 \, \log \left (x\right )}{4 \, a^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a^4 - x^4)*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.311318, size = 19, normalized size = 0.79 \[ \frac{\log{\left (x \right )}}{a^{4}} - \frac{\log{\left (- a^{4} + x^{4} \right )}}{4 a^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x/(a**4-x**4),x)
[Out]
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GIAC/XCAS [A] time = 0.202234, size = 35, normalized size = 1.46 \[ \frac{{\rm ln}\left (x^{4}\right )}{4 \, a^{4}} - \frac{{\rm ln}\left ({\left | -a^{4} + x^{4} \right |}\right )}{4 \, a^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a^4 - x^4)*x),x, algorithm="giac")
[Out]