Optimal. Leaf size=16 \[ \frac {3 x \log ^2(x)}{7-e^2} \]
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Rubi [A]
time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps
used = 5, number of rules used = 3, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.158, Rules used = {12, 2332, 2333}
\begin {gather*} \frac {3 x \log ^2(x)}{7-e^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2332
Rule 2333
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (-6 \log (x)-3 \log ^2(x)\right ) \, dx}{-7+e^2}\\ &=\frac {3 \int \log ^2(x) \, dx}{7-e^2}+\frac {6 \int \log (x) \, dx}{7-e^2}\\ &=-\frac {6 x}{7-e^2}+\frac {6 x \log (x)}{7-e^2}+\frac {3 x \log ^2(x)}{7-e^2}-\frac {6 \int \log (x) \, dx}{7-e^2}\\ &=\frac {3 x \log ^2(x)}{7-e^2}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 14, normalized size = 0.88 \begin {gather*} -\frac {3 x \log ^2(x)}{-7+e^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 14, normalized size = 0.88
method | result | size |
default | \(-\frac {3 x \ln \left (x \right )^{2}}{{\mathrm e}^{2}-7}\) | \(14\) |
norman | \(-\frac {3 x \ln \left (x \right )^{2}}{{\mathrm e}^{2}-7}\) | \(14\) |
risch | \(-\frac {3 x \ln \left (x \right )^{2}}{{\mathrm e}^{2}-7}\) | \(14\) |
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. 29 vs.
\(2 (13) = 26\).
time = 0.26, size = 29, normalized size = 1.81 \begin {gather*} -\frac {3 \, {\left ({\left (\log \left (x\right )^{2} - 2 \, \log \left (x\right ) + 2\right )} x + 2 \, x \log \left (x\right ) - 2 \, x\right )}}{e^{2} - 7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 13, normalized size = 0.81 \begin {gather*} -\frac {3 \, x \log \left (x\right )^{2}}{e^{2} - 7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 14, normalized size = 0.88 \begin {gather*} - \frac {3 x \log {\left (x \right )}^{2}}{-7 + e^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 13, normalized size = 0.81 \begin {gather*} -\frac {3 \, x \log \left (x\right )^{2}}{e^{2} - 7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 6.50, size = 13, normalized size = 0.81 \begin {gather*} -\frac {3\,x\,{\ln \left (x\right )}^2}{{\mathrm {e}}^2-7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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