Optimal. Leaf size=22 \[ \frac {1}{5} e^5 \left (-3+\frac {3}{\log \left (\frac {1}{2} x (3+x)\right )}\right ) \]
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Rubi [A]
time = 0.12, antiderivative size = 21, normalized size of antiderivative = 0.95, number of steps
used = 3, number of rules used = 3, integrand size = 34, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.088, Rules used = {12, 1607, 6818}
\begin {gather*} \frac {3 e^5}{5 \log \left (\frac {1}{2} \left (x^2+3 x\right )\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 1607
Rule 6818
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^5 \int \frac {-9-6 x}{\left (15 x+5 x^2\right ) \log ^2\left (\frac {1}{2} \left (3 x+x^2\right )\right )} \, dx\\ &=e^5 \int \frac {-9-6 x}{x (15+5 x) \log ^2\left (\frac {1}{2} \left (3 x+x^2\right )\right )} \, dx\\ &=\frac {3 e^5}{5 \log \left (\frac {1}{2} \left (3 x+x^2\right )\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 18, normalized size = 0.82 \begin {gather*} \frac {3 e^5}{5 \log \left (\frac {1}{2} x (3+x)\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.58, size = 20, normalized size = 0.91
method | result | size |
norman | \(\frac {3 \,{\mathrm e}^{5}}{5 \ln \left (\frac {1}{2} x^{2}+\frac {3}{2} x \right )}\) | \(17\) |
risch | \(\frac {3 \,{\mathrm e}^{5}}{5 \ln \left (\frac {1}{2} x^{2}+\frac {3}{2} x \right )}\) | \(17\) |
default | \(-\frac {3 \,{\mathrm e}^{5}}{5 \left (\ln \left (2\right )-\ln \left (x^{2}+3 x \right )\right )}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.54, size = 19, normalized size = 0.86 \begin {gather*} -\frac {3 \, e^{5}}{5 \, {\left (\log \left (2\right ) - \log \left (x + 3\right ) - \log \left (x\right )\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 16, normalized size = 0.73 \begin {gather*} \frac {3 \, e^{5}}{5 \, \log \left (\frac {1}{2} \, x^{2} + \frac {3}{2} \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 17, normalized size = 0.77 \begin {gather*} \frac {3 e^{5}}{5 \log {\left (\frac {x^{2}}{2} + \frac {3 x}{2} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 16, normalized size = 0.73 \begin {gather*} \frac {3 \, e^{5}}{5 \, \log \left (\frac {1}{2} \, x^{2} + \frac {3}{2} \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.70, size = 16, normalized size = 0.73 \begin {gather*} \frac {3\,{\mathrm {e}}^5}{5\,\ln \left (\frac {x^2}{2}+\frac {3\,x}{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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