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 = 0.01, antiderivative size = 24, normalized size of antiderivative = 1.00, 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 29
Rule 31
Rule 36
Rule 266
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*}
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Mathematica [A] time = 0.01, size = 24, normalized size = 1.00 \[ \frac {\log (x)}{a^4}-\frac {\log \left (x^4-a^4\right )}{4 a^4} \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.01, size = 24, normalized size = 1.00 \[ \frac {\log (x)}{a^4}-\frac {\log \left (a^4-x^4\right )}{4 a^4} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 20, normalized size = 0.83 \[ -\frac {\log \left (-a^{4} + x^{4}\right ) - 4 \, \log \relax (x)}{4 \, a^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.95, size = 26, normalized size = 1.08 \[ \frac {\log \left (x^{4}\right )}{4 \, a^{4}} - \frac {\log \left ({\left | -a^{4} + x^{4} \right |}\right )}{4 \, a^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.32, size = 23, normalized size = 0.96
method | result | size |
risch | \(\frac {\ln \relax (x )}{a^{4}}-\frac {\ln \left (-a^{4}+x^{4}\right )}{4 a^{4}}\) | \(23\) |
default | \(-\frac {\ln \left (a^{2}+x^{2}\right )}{4 a^{4}}+\frac {\ln \relax (x )}{a^{4}}-\frac {\ln \left (a +x \right )}{4 a^{4}}-\frac {\ln \left (a -x \right )}{4 a^{4}}\) | \(41\) |
norman | \(-\frac {\ln \left (a^{2}+x^{2}\right )}{4 a^{4}}+\frac {\ln \relax (x )}{a^{4}}-\frac {\ln \left (a +x \right )}{4 a^{4}}-\frac {\ln \left (a -x \right )}{4 a^{4}}\) | \(41\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 25, normalized size = 1.04 \[ -\frac {\log \left (-a^{4} + x^{4}\right )}{4 \, a^{4}} + \frac {\log \left (x^{4}\right )}{4 \, a^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.28, size = 20, normalized size = 0.83 \[ -\frac {\ln \left (x^4-a^4\right )-4\,\ln \relax (x)}{4\,a^4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.25, size = 19, normalized size = 0.79 \[ \frac {\log {\relax (x )}}{a^{4}} - \frac {\log {\left (- a^{4} + x^{4} \right )}}{4 a^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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