Optimal. Leaf size=13 \[ \frac {1125 \log ^2(2 x)}{16 x^2} \]
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Rubi [A]
time = 0.03, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps
used = 6, number of rules used = 4, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {12, 14, 2341,
2342} \begin {gather*} \frac {1125 \log ^2(2 x)}{16 x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2341
Rule 2342
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{8} \int \frac {1125 \log (2 x)-1125 \log ^2(2 x)}{x^3} \, dx\\ &=\frac {1}{8} \int \left (\frac {1125 \log (2 x)}{x^3}-\frac {1125 \log ^2(2 x)}{x^3}\right ) \, dx\\ &=\frac {1125}{8} \int \frac {\log (2 x)}{x^3} \, dx-\frac {1125}{8} \int \frac {\log ^2(2 x)}{x^3} \, dx\\ &=-\frac {1125}{32 x^2}-\frac {1125 \log (2 x)}{16 x^2}+\frac {1125 \log ^2(2 x)}{16 x^2}-\frac {1125}{8} \int \frac {\log (2 x)}{x^3} \, dx\\ &=\frac {1125 \log ^2(2 x)}{16 x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 13, normalized size = 1.00 \begin {gather*} \frac {1125 \log ^2(2 x)}{16 x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.14, size = 12, normalized size = 0.92
method | result | size |
derivativedivides | \(\frac {1125 \ln \left (2 x \right )^{2}}{16 x^{2}}\) | \(12\) |
default | \(\frac {1125 \ln \left (2 x \right )^{2}}{16 x^{2}}\) | \(12\) |
norman | \(\frac {1125 \ln \left (2 x \right )^{2}}{16 x^{2}}\) | \(12\) |
risch | \(\frac {1125 \ln \left (2 x \right )^{2}}{16 x^{2}}\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 35 vs.
\(2 (11) = 22\).
time = 0.27, size = 35, normalized size = 2.69 \begin {gather*} \frac {1125 \, {\left (2 \, \log \left (2 \, x\right )^{2} + 2 \, \log \left (2 \, x\right ) + 1\right )}}{32 \, x^{2}} - \frac {1125 \, {\left (2 \, \log \left (2 \, x\right ) + 1\right )}}{32 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 11, normalized size = 0.85 \begin {gather*} \frac {1125 \, \log \left (2 \, x\right )^{2}}{16 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 12, normalized size = 0.92 \begin {gather*} \frac {1125 \log {\left (2 x \right )}^{2}}{16 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 11, normalized size = 0.85 \begin {gather*} \frac {1125 \, \log \left (2 \, x\right )^{2}}{16 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.44, size = 11, normalized size = 0.85 \begin {gather*} \frac {1125\,{\ln \left (2\,x\right )}^2}{16\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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