Optimal. Leaf size=29 \[ -\frac {9-\frac {\frac {3}{2}+x}{-e^{5/3}+\log (3)}}{x}+\log (x) \]
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Rubi [A]
time = 0.05, antiderivative size = 35, normalized size of antiderivative = 1.21, number of steps
used = 5, number of rules used = 4, integrand size = 42, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.095, Rules used = {6, 12, 192, 45}
\begin {gather*} \log (x)-\frac {3 \left (1+6 e^{5/3}-6 \log (3)\right )}{x \left (2 e^{5/3}-\log (9)\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 45
Rule 192
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-3+e^{5/3} (-18-2 x)+(18+2 x) \log (3)}{x^2 \left (-2 e^{5/3}+2 \log (3)\right )} \, dx\\ &=\frac {\int \frac {-3+e^{5/3} (-18-2 x)+(18+2 x) \log (3)}{x^2} \, dx}{-2 e^{5/3}+2 \log (3)}\\ &=\frac {\int \frac {-3 \left (1+6 e^{5/3}-6 \log (3)\right )-2 x \left (e^{5/3}-\log (3)\right )}{x^2} \, dx}{-2 e^{5/3}+2 \log (3)}\\ &=\frac {\int \left (-\frac {3 \left (1+6 e^{5/3}-6 \log (3)\right )}{x^2}+\frac {-2 e^{5/3}+\log (9)}{x}\right ) \, dx}{-2 e^{5/3}+2 \log (3)}\\ &=-\frac {3 \left (1+6 e^{5/3}-6 \log (3)\right )}{x \left (2 e^{5/3}-\log (9)\right )}+\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 50, normalized size = 1.72 \begin {gather*} \frac {-\frac {3 \left (1+6 e^{5/3}-6 \log (3)\right )}{x}+\left (2 e^{5/3}-\log (9)\right ) \log (x)}{2 \left (e^{5/3}-\log (3)\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.72, size = 40, normalized size = 1.38
method | result | size |
norman | \(-\frac {3 \left (6 \ln \left (3\right )-6 \,{\mathrm e}^{\frac {5}{3}}-1\right )}{2 \left (\ln \left (3\right )-{\mathrm e}^{\frac {5}{3}}\right ) x}+\ln \left (x \right )\) | \(28\) |
default | \(\frac {-\frac {18 \ln \left (3\right )-18 \,{\mathrm e}^{\frac {5}{3}}-3}{x}+\left (2 \ln \left (3\right )-2 \,{\mathrm e}^{\frac {5}{3}}\right ) \ln \left (x \right )}{2 \ln \left (3\right )-2 \,{\mathrm e}^{\frac {5}{3}}}\) | \(40\) |
risch | \(-\frac {9 \ln \left (3\right )}{x \left (\ln \left (3\right )-{\mathrm e}^{\frac {5}{3}}\right )}+\frac {9 \,{\mathrm e}^{\frac {5}{3}}}{x \left (\ln \left (3\right )-{\mathrm e}^{\frac {5}{3}}\right )}+\frac {3}{2 x \left (\ln \left (3\right )-{\mathrm e}^{\frac {5}{3}}\right )}+\ln \left (x \right )\) | \(50\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 27, normalized size = 0.93 \begin {gather*} -\frac {3 \, {\left (6 \, e^{\frac {5}{3}} - 6 \, \log \left (3\right ) + 1\right )}}{2 \, x {\left (e^{\frac {5}{3}} - \log \left (3\right )\right )}} + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 38, normalized size = 1.31 \begin {gather*} \frac {2 \, {\left (x e^{\frac {5}{3}} - x \log \left (3\right )\right )} \log \left (x\right ) - 18 \, e^{\frac {5}{3}} + 18 \, \log \left (3\right ) - 3}{2 \, {\left (x e^{\frac {5}{3}} - x \log \left (3\right )\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 39 vs.
\(2 (19) = 38\).
time = 0.13, size = 39, normalized size = 1.34 \begin {gather*} \frac {2 \left (- \log {\left (3 \right )} + e^{\frac {5}{3}}\right ) \log {\left (x \right )} + \frac {- 18 e^{\frac {5}{3}} - 3 + 18 \log {\left (3 \right )}}{x}}{- 2 \log {\left (3 \right )} + 2 e^{\frac {5}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.43, size = 28, normalized size = 0.97 \begin {gather*} -\frac {3 \, {\left (6 \, e^{\frac {5}{3}} - 6 \, \log \left (3\right ) + 1\right )}}{2 \, x {\left (e^{\frac {5}{3}} - \log \left (3\right )\right )}} + \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.11, size = 29, normalized size = 1.00 \begin {gather*} \ln \left (x\right )-\frac {18\,{\mathrm {e}}^{5/3}-18\,\ln \left (3\right )+3}{x\,\left (2\,{\mathrm {e}}^{5/3}-\ln \left (9\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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