Optimal. Leaf size=13 \[ \log ^2\left (x-\frac {e^5 x}{3}\right ) \]
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Rubi [A]
time = 0.02, antiderivative size = 15, normalized size of antiderivative = 1.15, number of steps
used = 3, number of rules used = 3, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.150, Rules used = {12, 2468, 2338}
\begin {gather*} \log ^2\left (\frac {1}{3} \left (3-e^5\right ) x\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2338
Rule 2468
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=2 \int \frac {\log \left (\frac {1}{3} \left (3 x-e^5 x\right )\right )}{x} \, dx\\ &=2 \int \frac {\log \left (\frac {1}{3} \left (3-e^5\right ) x\right )}{x} \, dx\\ &=\log ^2\left (\frac {1}{3} \left (3-e^5\right ) x\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 25, normalized size = 1.92 \begin {gather*} 2 \left (-\frac {1}{2} \log ^2(x)+\log (x) \log \left (x-\frac {e^5 x}{3}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.17, size = 12, normalized size = 0.92
method | result | size |
norman | \(\ln \left (-\frac {x \,{\mathrm e}^{5}}{3}+x \right )^{2}\) | \(11\) |
risch | \(\ln \left (-\frac {x \,{\mathrm e}^{5}}{3}+x \right )^{2}\) | \(11\) |
derivativedivides | \(\ln \left (\left (-\frac {{\mathrm e}^{5}}{3}+1\right ) x \right )^{2}\) | \(12\) |
default | \(\ln \left (\left (-\frac {{\mathrm e}^{5}}{3}+1\right ) x \right )^{2}\) | \(12\) |
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. 21 vs.
\(2 (10) = 20\).
time = 0.47, size = 21, normalized size = 1.62 \begin {gather*} -2 \, {\left (\log \left (3\right ) - \log \left (-e^{5} + 3\right )\right )} \log \left (x\right ) + \log \left (x\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 10, normalized size = 0.77 \begin {gather*} \log \left (-\frac {1}{3} \, x e^{5} + x\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 10, normalized size = 0.77 \begin {gather*} \log {\left (- \frac {x e^{5}}{3} + x \right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 10, normalized size = 0.77 \begin {gather*} \log \left (-\frac {1}{3} \, x e^{5} + x\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.02, size = 10, normalized size = 0.77 \begin {gather*} {\ln \left (x-\frac {x\,{\mathrm {e}}^5}{3}\right )}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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