Optimal. Leaf size=19 \[ -\frac {1}{2 x^2}-\frac {\log \left (x^2\right )}{2 x^2} \]
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Rubi [A]
time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {2341}
\begin {gather*} -\frac {1}{2 x^2}-\frac {\log \left (x^2\right )}{2 x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 2341
Rubi steps
\begin {align*} \int \frac {\log \left (x^2\right )}{x^3} \, dx &=-\frac {1}{2 x^2}-\frac {\log \left (x^2\right )}{2 x^2}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 19, normalized size = 1.00 \begin {gather*} -\frac {1}{2 x^2}-\frac {\log \left (x^2\right )}{2 x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 16, normalized size = 0.84
method | result | size |
norman | \(\frac {-\frac {1}{2}-\frac {\ln \left (x^{2}\right )}{2}}{x^{2}}\) | \(13\) |
default | \(-\frac {1}{2 x^{2}}-\frac {\ln \left (x^{2}\right )}{2 x^{2}}\) | \(16\) |
risch | \(-\frac {1}{2 x^{2}}-\frac {\ln \left (x^{2}\right )}{2 x^{2}}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 1.56, size = 15, normalized size = 0.79 \begin {gather*} -\frac {\log \left (x^{2}\right )}{2 \, x^{2}} - \frac {1}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.55, size = 11, normalized size = 0.58 \begin {gather*} -\frac {\log \left (x^{2}\right ) + 1}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 17, normalized size = 0.89 \begin {gather*} - \frac {\log {\left (x^{2} \right )}}{2 x^{2}} - \frac {1}{2 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 15, normalized size = 0.79 \begin {gather*} -\frac {\log \left (x^{2}\right )}{2 \, x^{2}} - \frac {1}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.16, size = 11, normalized size = 0.58 \begin {gather*} -\frac {\ln \left (x^2\right )+1}{2\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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