Optimal. Leaf size=23 \[ -\frac {6 e^4 x}{3-x}+\log \left (5 e^4 x^3\right ) \]
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Rubi [A] time = 0.03, antiderivative size = 17, normalized size of antiderivative = 0.74, number of steps used = 5, number of rules used = 4, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.129, Rules used = {6, 1594, 27, 893} \begin {gather*} 3 \log (x)-\frac {18 e^4}{3-x} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 27
Rule 893
Rule 1594
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {27+\left (-18-18 e^4\right ) x+3 x^2}{9 x-6 x^2+x^3} \, dx\\ &=\int \frac {27+\left (-18-18 e^4\right ) x+3 x^2}{x \left (9-6 x+x^2\right )} \, dx\\ &=\int \frac {27+\left (-18-18 e^4\right ) x+3 x^2}{(-3+x)^2 x} \, dx\\ &=\int \left (-\frac {18 e^4}{(-3+x)^2}+\frac {3}{x}\right ) \, dx\\ &=-\frac {18 e^4}{3-x}+3 \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 15, normalized size = 0.65 \begin {gather*} 3 \left (\frac {6 e^4}{-3+x}+\log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.54, size = 18, normalized size = 0.78 \begin {gather*} \frac {3 \, {\left ({\left (x - 3\right )} \log \relax (x) + 6 \, e^{4}\right )}}{x - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.24, size = 15, normalized size = 0.65 \begin {gather*} \frac {18 \, e^{4}}{x - 3} + 3 \, \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 15, normalized size = 0.65
method | result | size |
default | \(3 \ln \relax (x )+\frac {18 \,{\mathrm e}^{4}}{x -3}\) | \(15\) |
norman | \(3 \ln \relax (x )+\frac {18 \,{\mathrm e}^{4}}{x -3}\) | \(15\) |
risch | \(3 \ln \relax (x )+\frac {18 \,{\mathrm e}^{4}}{x -3}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 14, normalized size = 0.61 \begin {gather*} \frac {18 \, e^{4}}{x - 3} + 3 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 14, normalized size = 0.61 \begin {gather*} 3\,\ln \relax (x)+\frac {18\,{\mathrm {e}}^4}{x-3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 12, normalized size = 0.52 \begin {gather*} 3 \log {\relax (x )} + \frac {18 e^{4}}{x - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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