Integrand size = 50, antiderivative size = 23 \[ \int \frac {100+250 x-37 x^2-3 x^3+e^x \left (-75 x+27 x^2+x^3\right )+\left (-25 x-2 x^2\right ) \log (x)}{25 x} \, dx=\left (4-x-\frac {x^2}{25}\right ) \left (-7-e^x+x+\log (x)\right ) \]
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Leaf count is larger than twice the leaf count of optimal. \(56\) vs. \(2(23)=46\).
Time = 0.06 (sec) , antiderivative size = 56, normalized size of antiderivative = 2.43, number of steps used = 17, number of rules used = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.120, Rules used = {12, 14, 2227, 2225, 2207, 2350} \[ \int \frac {100+250 x-37 x^2-3 x^3+e^x \left (-75 x+27 x^2+x^3\right )+\left (-25 x-2 x^2\right ) \log (x)}{25 x} \, dx=-\frac {x^3}{25}+\frac {e^x x^2}{25}-\frac {18 x^2}{25}-\frac {1}{25} x^2 \log (x)+e^x x+11 x-4 e^x-x \log (x)+4 \log (x) \]
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Rule 12
Rule 14
Rule 2207
Rule 2225
Rule 2227
Rule 2350
Rubi steps \begin{align*} \text {integral}& = \frac {1}{25} \int \frac {100+250 x-37 x^2-3 x^3+e^x \left (-75 x+27 x^2+x^3\right )+\left (-25 x-2 x^2\right ) \log (x)}{x} \, dx \\ & = \frac {1}{25} \int \left (e^x \left (-75+27 x+x^2\right )+\frac {100+250 x-37 x^2-3 x^3-25 x \log (x)-2 x^2 \log (x)}{x}\right ) \, dx \\ & = \frac {1}{25} \int e^x \left (-75+27 x+x^2\right ) \, dx+\frac {1}{25} \int \frac {100+250 x-37 x^2-3 x^3-25 x \log (x)-2 x^2 \log (x)}{x} \, dx \\ & = \frac {1}{25} \int \left (-75 e^x+27 e^x x+e^x x^2\right ) \, dx+\frac {1}{25} \int \left (\frac {100+250 x-37 x^2-3 x^3}{x}-(25+2 x) \log (x)\right ) \, dx \\ & = \frac {1}{25} \int e^x x^2 \, dx+\frac {1}{25} \int \frac {100+250 x-37 x^2-3 x^3}{x} \, dx-\frac {1}{25} \int (25+2 x) \log (x) \, dx+\frac {27}{25} \int e^x x \, dx-3 \int e^x \, dx \\ & = -3 e^x+\frac {27 e^x x}{25}+\frac {e^x x^2}{25}-x \log (x)-\frac {1}{25} x^2 \log (x)+\frac {1}{25} \int (25+x) \, dx+\frac {1}{25} \int \left (250+\frac {100}{x}-37 x-3 x^2\right ) \, dx-\frac {2}{25} \int e^x x \, dx-\frac {27 \int e^x \, dx}{25} \\ & = -\frac {102 e^x}{25}+11 x+e^x x-\frac {18 x^2}{25}+\frac {e^x x^2}{25}-\frac {x^3}{25}+4 \log (x)-x \log (x)-\frac {1}{25} x^2 \log (x)+\frac {2 \int e^x \, dx}{25} \\ & = -4 e^x+11 x+e^x x-\frac {18 x^2}{25}+\frac {e^x x^2}{25}-\frac {x^3}{25}+4 \log (x)-x \log (x)-\frac {1}{25} x^2 \log (x) \\ \end{align*}
Time = 0.08 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.83 \[ \int \frac {100+250 x-37 x^2-3 x^3+e^x \left (-75 x+27 x^2+x^3\right )+\left (-25 x-2 x^2\right ) \log (x)}{25 x} \, dx=\frac {1}{25} \left (275 x-18 x^2-x^3+e^x \left (-100+25 x+x^2\right )+100 \log (x)-x (25+x) \log (x)\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(45\) vs. \(2(20)=40\).
Time = 0.04 (sec) , antiderivative size = 46, normalized size of antiderivative = 2.00
method | result | size |
default | \(-\frac {x^{2} \ln \left (x \right )}{25}-\frac {18 x^{2}}{25}-x \ln \left (x \right )+11 x +\frac {{\mathrm e}^{x} x^{2}}{25}+{\mathrm e}^{x} x -4 \,{\mathrm e}^{x}-\frac {x^{3}}{25}+4 \ln \left (x \right )\) | \(46\) |
norman | \(-\frac {x^{2} \ln \left (x \right )}{25}-\frac {18 x^{2}}{25}-x \ln \left (x \right )+11 x +\frac {{\mathrm e}^{x} x^{2}}{25}+{\mathrm e}^{x} x -4 \,{\mathrm e}^{x}-\frac {x^{3}}{25}+4 \ln \left (x \right )\) | \(46\) |
parallelrisch | \(-\frac {x^{2} \ln \left (x \right )}{25}-\frac {18 x^{2}}{25}-x \ln \left (x \right )+11 x +\frac {{\mathrm e}^{x} x^{2}}{25}+{\mathrm e}^{x} x -4 \,{\mathrm e}^{x}-\frac {x^{3}}{25}+4 \ln \left (x \right )\) | \(46\) |
parts | \(-\frac {x^{2} \ln \left (x \right )}{25}-\frac {18 x^{2}}{25}-x \ln \left (x \right )+11 x +\frac {{\mathrm e}^{x} x^{2}}{25}+{\mathrm e}^{x} x -4 \,{\mathrm e}^{x}-\frac {x^{3}}{25}+4 \ln \left (x \right )\) | \(46\) |
risch | \(\frac {\left (-x^{2}-25 x \right ) \ln \left (x \right )}{25}-\frac {x^{3}}{25}+\frac {{\mathrm e}^{x} x^{2}}{25}-\frac {18 x^{2}}{25}+{\mathrm e}^{x} x +4 \ln \left (x \right )+11 x -4 \,{\mathrm e}^{x}\) | \(47\) |
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Time = 0.27 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.65 \[ \int \frac {100+250 x-37 x^2-3 x^3+e^x \left (-75 x+27 x^2+x^3\right )+\left (-25 x-2 x^2\right ) \log (x)}{25 x} \, dx=-\frac {1}{25} \, x^{3} - \frac {18}{25} \, x^{2} + \frac {1}{25} \, {\left (x^{2} + 25 \, x - 100\right )} e^{x} - \frac {1}{25} \, {\left (x^{2} + 25 \, x - 100\right )} \log \left (x\right ) + 11 \, x \]
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Leaf count of result is larger than twice the leaf count of optimal. 44 vs. \(2 (17) = 34\).
Time = 0.12 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.91 \[ \int \frac {100+250 x-37 x^2-3 x^3+e^x \left (-75 x+27 x^2+x^3\right )+\left (-25 x-2 x^2\right ) \log (x)}{25 x} \, dx=- \frac {x^{3}}{25} - \frac {18 x^{2}}{25} + 11 x + \left (- \frac {x^{2}}{25} - x\right ) \log {\left (x \right )} + \frac {\left (x^{2} + 25 x - 100\right ) e^{x}}{25} + 4 \log {\left (x \right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 53 vs. \(2 (19) = 38\).
Time = 0.19 (sec) , antiderivative size = 53, normalized size of antiderivative = 2.30 \[ \int \frac {100+250 x-37 x^2-3 x^3+e^x \left (-75 x+27 x^2+x^3\right )+\left (-25 x-2 x^2\right ) \log (x)}{25 x} \, dx=-\frac {1}{25} \, x^{3} - \frac {1}{25} \, x^{2} \log \left (x\right ) - \frac {18}{25} \, x^{2} + \frac {1}{25} \, {\left (x^{2} - 2 \, x + 2\right )} e^{x} + \frac {27}{25} \, {\left (x - 1\right )} e^{x} - x \log \left (x\right ) + 11 \, x - 3 \, e^{x} + 4 \, \log \left (x\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 45 vs. \(2 (19) = 38\).
Time = 0.29 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.96 \[ \int \frac {100+250 x-37 x^2-3 x^3+e^x \left (-75 x+27 x^2+x^3\right )+\left (-25 x-2 x^2\right ) \log (x)}{25 x} \, dx=-\frac {1}{25} \, x^{3} + \frac {1}{25} \, x^{2} e^{x} - \frac {1}{25} \, x^{2} \log \left (x\right ) - \frac {18}{25} \, x^{2} + x e^{x} - x \log \left (x\right ) + 11 \, x - 4 \, e^{x} + 4 \, \log \left (x\right ) \]
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Time = 8.05 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.96 \[ \int \frac {100+250 x-37 x^2-3 x^3+e^x \left (-75 x+27 x^2+x^3\right )+\left (-25 x-2 x^2\right ) \log (x)}{25 x} \, dx=11\,x-4\,{\mathrm {e}}^x+4\,\ln \left (x\right )+\frac {x^2\,{\mathrm {e}}^x}{25}-\frac {x^2\,\ln \left (x\right )}{25}+x\,{\mathrm {e}}^x-x\,\ln \left (x\right )-\frac {18\,x^2}{25}-\frac {x^3}{25} \]
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