Integrand size = 30, antiderivative size = 18 \[ \int \frac {e^x \left (-1+7 x+x^2-x^3\right )-e^x x \log (x)}{x} \, dx=e^x \left (4+3 x-x^2-\log (x)\right ) \]
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Time = 0.04 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.50, number of steps used = 11, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {14, 2225, 2209, 2207, 2634} \[ \int \frac {e^x \left (-1+7 x+x^2-x^3\right )-e^x x \log (x)}{x} \, dx=-e^x x^2+3 e^x x+4 e^x-e^x \log (x) \]
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Rule 14
Rule 2207
Rule 2209
Rule 2225
Rule 2634
Rubi steps \begin{align*} \text {integral}& = \int \left (7 e^x-\frac {e^x}{x}+e^x x-e^x x^2-e^x \log (x)\right ) \, dx \\ & = 7 \int e^x \, dx-\int \frac {e^x}{x} \, dx+\int e^x x \, dx-\int e^x x^2 \, dx-\int e^x \log (x) \, dx \\ & = 7 e^x+e^x x-e^x x^2-\operatorname {ExpIntegralEi}(x)-e^x \log (x)+2 \int e^x x \, dx-\int e^x \, dx+\int \frac {e^x}{x} \, dx \\ & = 6 e^x+3 e^x x-e^x x^2-e^x \log (x)-2 \int e^x \, dx \\ & = 4 e^x+3 e^x x-e^x x^2-e^x \log (x) \\ \end{align*}
Time = 0.06 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.83 \[ \int \frac {e^x \left (-1+7 x+x^2-x^3\right )-e^x x \log (x)}{x} \, dx=-e^x \left (-4-3 x+x^2+\log (x)\right ) \]
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Time = 0.07 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11
method | result | size |
risch | \(-{\mathrm e}^{x} \ln \left (x \right )-\left (x^{2}-3 x -4\right ) {\mathrm e}^{x}\) | \(20\) |
norman | \(3 \,{\mathrm e}^{x} x -{\mathrm e}^{x} x^{2}-{\mathrm e}^{x} \ln \left (x \right )+4 \,{\mathrm e}^{x}\) | \(24\) |
parallelrisch | \(3 \,{\mathrm e}^{x} x -{\mathrm e}^{x} x^{2}-{\mathrm e}^{x} \ln \left (x \right )+4 \,{\mathrm e}^{x}\) | \(24\) |
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Time = 0.27 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.06 \[ \int \frac {e^x \left (-1+7 x+x^2-x^3\right )-e^x x \log (x)}{x} \, dx=-{\left (x^{2} - 3 \, x - 4\right )} e^{x} - e^{x} \log \left (x\right ) \]
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Time = 0.10 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.78 \[ \int \frac {e^x \left (-1+7 x+x^2-x^3\right )-e^x x \log (x)}{x} \, dx=\left (- x^{2} + 3 x - \log {\left (x \right )} + 4\right ) e^{x} \]
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Leaf count of result is larger than twice the leaf count of optimal. 29 vs. \(2 (14) = 28\).
Time = 0.22 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.61 \[ \int \frac {e^x \left (-1+7 x+x^2-x^3\right )-e^x x \log (x)}{x} \, dx=-{\left (x^{2} - 2 \, x + 2\right )} e^{x} + {\left (x - 1\right )} e^{x} - e^{x} \log \left (x\right ) + 7 \, e^{x} \]
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Time = 0.28 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.28 \[ \int \frac {e^x \left (-1+7 x+x^2-x^3\right )-e^x x \log (x)}{x} \, dx=-x^{2} e^{x} + 3 \, x e^{x} - e^{x} \log \left (x\right ) + 4 \, e^{x} \]
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Time = 13.07 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.94 \[ \int \frac {e^x \left (-1+7 x+x^2-x^3\right )-e^x x \log (x)}{x} \, dx={\mathrm {e}}^x\,\left (3\,x-\ln \left (x\right )-x^2+4\right ) \]
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