Optimal. Leaf size=17 \[ -\frac {1}{16 x^4}-\frac {\log (x)}{4 x^4} \]
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Rubi [A]
time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {2341}
\begin {gather*} -\frac {1}{16 x^4}-\frac {\log (x)}{4 x^4} \end {gather*}
Antiderivative was successfully verified.
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Rule 2341
Rubi steps
\begin {align*} \int \frac {\log (x)}{x^5} \, dx &=-\frac {1}{16 x^4}-\frac {\log (x)}{4 x^4}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 17, normalized size = 1.00 \begin {gather*} -\frac {1}{16 x^4}-\frac {\log (x)}{4 x^4} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 14, normalized size = 0.82
method | result | size |
norman | \(\frac {-\frac {1}{16}-\frac {\ln \left (x \right )}{4}}{x^{4}}\) | \(11\) |
default | \(-\frac {1}{16 x^{4}}-\frac {\ln \left (x \right )}{4 x^{4}}\) | \(14\) |
risch | \(-\frac {1}{16 x^{4}}-\frac {\ln \left (x \right )}{4 x^{4}}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.43, size = 13, normalized size = 0.76 \begin {gather*} -\frac {\log \left (x\right )}{4 \, x^{4}} - \frac {1}{16 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.66, size = 11, normalized size = 0.65 \begin {gather*} -\frac {4 \, \log \left (x\right ) + 1}{16 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 15, normalized size = 0.88 \begin {gather*} - \frac {\log {\left (x \right )}}{4 x^{4}} - \frac {1}{16 x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.78, size = 13, normalized size = 0.76 \begin {gather*} -\frac {\log \left (x\right )}{4 \, x^{4}} - \frac {1}{16 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.17, size = 9, normalized size = 0.53 \begin {gather*} -\frac {\ln \left (x\right )+\frac {1}{4}}{4\,x^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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