Optimal. Leaf size=23 \[ 1-\frac {2+x}{e}-\frac {x}{5 (-4+3 \log (3))} \]
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Rubi [A] time = 0.02, antiderivative size = 17, normalized size of antiderivative = 0.74, 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 = {186, 21, 8} \begin {gather*} -\frac {1}{5} x \left (\frac {5}{e}+\frac {1}{\log (27)-4}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 8
Rule 21
Rule 186
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\frac {2 (20-e-5 \log (27))}{e}+\frac {x (20-e-5 \log (27))}{e}}{-10 (4-3 \log (3))-5 x (4-\log (27))} \, dx\\ &=-\left (\frac {1}{5} \left (\frac {5}{e}+\frac {1}{-4+\log (27)}\right ) \int 1 \, dx\right )\\ &=-\frac {1}{5} x \left (\frac {5}{e}+\frac {1}{-4+\log (27)}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 18, normalized size = 0.78 \begin {gather*} x \left (-\frac {1}{e}-\frac {1}{5 (-4+\log (27))}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 28, normalized size = 1.22 \begin {gather*} -\frac {x e + 15 \, x \log \relax (3) - 20 \, x}{5 \, {\left (3 \, e \log \relax (3) - 4 \, e\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.31, size = 28, normalized size = 1.22 \begin {gather*} -\frac {x e + 15 \, x \log \relax (3) - 20 \, x}{5 \, {\left (3 \, e \log \relax (3) - 4 \, e\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.43, size = 22, normalized size = 0.96
method | result | size |
default | \(-\frac {x}{5 \left (3 \ln \relax (3)-4\right )}-{\mathrm e}^{\ln \left (2+x \right )-1}\) | \(22\) |
norman | \(-\frac {{\mathrm e}^{-1} \left ({\mathrm e}+15 \ln \relax (3)-20\right ) x}{5 \left (3 \ln \relax (3)-4\right )}\) | \(24\) |
risch | \(-\frac {15 x \ln \relax (3) {\mathrm e}^{-1}}{15 \ln \relax (3)-20}+\frac {20 x \,{\mathrm e}^{-1}}{15 \ln \relax (3)-20}-\frac {x}{15 \ln \relax (3)-20}\) | \(41\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 24, normalized size = 1.04 \begin {gather*} -\frac {x {\left (e + 15 \, \log \relax (3) - 20\right )}}{5 \, {\left (3 \, e \log \relax (3) - 4 \, e\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 23, normalized size = 1.00 \begin {gather*} \frac {x\,\left (\mathrm {e}+15\,\ln \relax (3)-20\right )}{20\,\mathrm {e}-15\,\mathrm {e}\,\ln \relax (3)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 24, normalized size = 1.04 \begin {gather*} \frac {x \left (- 15 \log {\relax (3 )} - e + 20\right )}{- 20 e + 15 e \log {\relax (3 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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