Optimal. Leaf size=24 \[ \frac{\log (x)}{a^4}-\frac{\log \left (a^4-x^4\right )}{4 a^4} \]
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Rubi [A] time = 0.0099267, 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, Rules used = {266, 36, 31, 29} \[ \frac{\log (x)}{a^4}-\frac{\log \left (a^4-x^4\right )}{4 a^4} \]
Antiderivative was successfully verified.
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Rule 266
Rule 36
Rule 31
Rule 29
Rubi steps
\begin{align*} \int \frac{1}{x \left (a^4-x^4\right )} \, dx &=\frac{1}{4} \operatorname{Subst}\left (\int \frac{1}{\left (a^4-x\right ) x} \, dx,x,x^4\right )\\ &=\frac{\operatorname{Subst}\left (\int \frac{1}{a^4-x} \, dx,x,x^4\right )}{4 a^4}+\frac{\operatorname{Subst}\left (\int \frac{1}{x} \, dx,x,x^4\right )}{4 a^4}\\ &=\frac{\log (x)}{a^4}-\frac{\log \left (a^4-x^4\right )}{4 a^4}\\ \end{align*}
Mathematica [A] time = 0.0054005, 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.
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Maple [A] time = 0.008, size = 41, normalized size = 1.7 \begin{align*}{\frac{\ln \left ( x \right ) }{{a}^{4}}}-{\frac{\ln \left ( -a+x \right ) }{4\,{a}^{4}}}-{\frac{\ln \left ({a}^{2}+{x}^{2} \right ) }{4\,{a}^{4}}}-{\frac{\ln \left ( a+x \right ) }{4\,{a}^{4}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.917133, size = 34, normalized size = 1.42 \begin{align*} -\frac{\log \left (-a^{4} + x^{4}\right )}{4 \, a^{4}} + \frac{\log \left (x^{4}\right )}{4 \, a^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.69358, size = 53, normalized size = 2.21 \begin{align*} -\frac{\log \left (-a^{4} + x^{4}\right ) - 4 \, \log \left (x\right )}{4 \, a^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.212124, size = 19, normalized size = 0.79 \begin{align*} \frac{\log{\left (x \right )}}{a^{4}} - \frac{\log{\left (- a^{4} + x^{4} \right )}}{4 a^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.0444, size = 35, normalized size = 1.46 \begin{align*} \frac{\log \left (x^{4}\right )}{4 \, a^{4}} - \frac{\log \left ({\left | -a^{4} + x^{4} \right |}\right )}{4 \, a^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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