Integrand size = 57, antiderivative size = 31 \[ \int \frac {e^{\frac {1}{3} \left (5-\log \left (6 x^2-x^3\right )\right )} (-4+x)-18 x+3 x^2+\left (6 x-x^2\right ) \log (20)}{-6 x+x^2} \, dx=-e^{\frac {1}{3} \left (5-\log \left ((6-x) x^2\right )\right )}+3 x-x \log (20) \]
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Time = 0.63 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {1607, 6874, 1602} \[ \int \frac {e^{\frac {1}{3} \left (5-\log \left (6 x^2-x^3\right )\right )} (-4+x)-18 x+3 x^2+\left (6 x-x^2\right ) \log (20)}{-6 x+x^2} \, dx=x (3-\log (20))-\frac {e^{5/3}}{\sqrt [3]{6 x^2-x^3}} \]
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Rule 1602
Rule 1607
Rule 6874
Rubi steps \begin{align*} \text {integral}& = \int \frac {e^{\frac {1}{3} \left (5-\log \left (6 x^2-x^3\right )\right )} (-4+x)-18 x+3 x^2+\left (6 x-x^2\right ) \log (20)}{(-6+x) x} \, dx \\ & = \int \left (\frac {e^{5/3} (4-x) x}{\left (6 x^2-x^3\right )^{4/3}}+3 \left (1-\frac {\log (20)}{3}\right )\right ) \, dx \\ & = x (3-\log (20))+e^{5/3} \int \frac {(4-x) x}{\left (6 x^2-x^3\right )^{4/3}} \, dx \\ & = -\frac {e^{5/3}}{\sqrt [3]{6 x^2-x^3}}+x (3-\log (20)) \\ \end{align*}
Time = 0.19 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.87 \[ \int \frac {e^{\frac {1}{3} \left (5-\log \left (6 x^2-x^3\right )\right )} (-4+x)-18 x+3 x^2+\left (6 x-x^2\right ) \log (20)}{-6 x+x^2} \, dx=-\frac {e^{5/3}}{\sqrt [3]{-\left ((-6+x) x^2\right )}}-x (-3+\log (20)) \]
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Time = 0.11 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.94
method | result | size |
default | \(3 x -{\mathrm e}^{-\frac {\ln \left (-x^{3}+6 x^{2}\right )}{3}+\frac {5}{3}}-x \ln \left (20\right )\) | \(29\) |
parts | \(3 x -{\mathrm e}^{-\frac {\ln \left (-x^{3}+6 x^{2}\right )}{3}+\frac {5}{3}}-x \ln \left (20\right )\) | \(29\) |
parallelrisch | \(-x \ln \left (20\right )+36-12 \ln \left (20\right )+3 x -{\mathrm e}^{-\frac {\ln \left (-x^{3}+6 x^{2}\right )}{3}+\frac {5}{3}}\) | \(34\) |
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Leaf count of result is larger than twice the leaf count of optimal. 52 vs. \(2 (25) = 50\).
Time = 0.25 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.68 \[ \int \frac {e^{\frac {1}{3} \left (5-\log \left (6 x^2-x^3\right )\right )} (-4+x)-18 x+3 x^2+\left (6 x-x^2\right ) \log (20)}{-6 x+x^2} \, dx=\frac {3 \, x^{4} - 18 \, x^{3} - {\left (x^{4} - 6 \, x^{3}\right )} \log \left (20\right ) + {\left (-x^{3} + 6 \, x^{2}\right )}^{\frac {2}{3}} e^{\frac {5}{3}}}{x^{3} - 6 \, x^{2}} \]
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\[ \int \frac {e^{\frac {1}{3} \left (5-\log \left (6 x^2-x^3\right )\right )} (-4+x)-18 x+3 x^2+\left (6 x-x^2\right ) \log (20)}{-6 x+x^2} \, dx=- \int \frac {4 e^{\frac {5}{3}}}{x^{2} \sqrt [3]{- x^{3} + 6 x^{2}} - 6 x \sqrt [3]{- x^{3} + 6 x^{2}}}\, dx - \int \frac {18 x \sqrt [3]{- x^{3} + 6 x^{2}}}{x^{2} \sqrt [3]{- x^{3} + 6 x^{2}} - 6 x \sqrt [3]{- x^{3} + 6 x^{2}}}\, dx - \int \left (- \frac {x e^{\frac {5}{3}}}{x^{2} \sqrt [3]{- x^{3} + 6 x^{2}} - 6 x \sqrt [3]{- x^{3} + 6 x^{2}}}\right )\, dx - \int \left (- \frac {3 x^{2} \sqrt [3]{- x^{3} + 6 x^{2}}}{x^{2} \sqrt [3]{- x^{3} + 6 x^{2}} - 6 x \sqrt [3]{- x^{3} + 6 x^{2}}}\right )\, dx - \int \left (- \frac {6 x \sqrt [3]{- x^{3} + 6 x^{2}} \log {\left (20 \right )}}{x^{2} \sqrt [3]{- x^{3} + 6 x^{2}} - 6 x \sqrt [3]{- x^{3} + 6 x^{2}}}\right )\, dx - \int \frac {x^{2} \sqrt [3]{- x^{3} + 6 x^{2}} \log {\left (20 \right )}}{x^{2} \sqrt [3]{- x^{3} + 6 x^{2}} - 6 x \sqrt [3]{- x^{3} + 6 x^{2}}}\, dx \]
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\[ \int \frac {e^{\frac {1}{3} \left (5-\log \left (6 x^2-x^3\right )\right )} (-4+x)-18 x+3 x^2+\left (6 x-x^2\right ) \log (20)}{-6 x+x^2} \, dx=\int { \frac {3 \, x^{2} + {\left (x - 4\right )} e^{\left (-\frac {1}{3} \, \log \left (-x^{3} + 6 \, x^{2}\right ) + \frac {5}{3}\right )} - {\left (x^{2} - 6 \, x\right )} \log \left (20\right ) - 18 \, x}{x^{2} - 6 \, x} \,d x } \]
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none
Time = 0.30 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.87 \[ \int \frac {e^{\frac {1}{3} \left (5-\log \left (6 x^2-x^3\right )\right )} (-4+x)-18 x+3 x^2+\left (6 x-x^2\right ) \log (20)}{-6 x+x^2} \, dx=-x {\left (\log \left (20\right ) - 3\right )} - e^{\left (-\frac {1}{3} \, \log \left (-x^{3} + 6 \, x^{2}\right ) + \frac {5}{3}\right )} \]
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Timed out. \[ \int \frac {e^{\frac {1}{3} \left (5-\log \left (6 x^2-x^3\right )\right )} (-4+x)-18 x+3 x^2+\left (6 x-x^2\right ) \log (20)}{-6 x+x^2} \, dx=-\int \frac {\ln \left (20\right )\,\left (6\,x-x^2\right )-18\,x+{\mathrm {e}}^{\frac {5}{3}-\frac {\ln \left (6\,x^2-x^3\right )}{3}}\,\left (x-4\right )+3\,x^2}{6\,x-x^2} \,d x \]
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