Integrand size = 139, antiderivative size = 34 \[ \int \frac {135-72 x+90 x^2-12 x^3-x^4+4 x^6+e^{2 e^2} \left (15-3 x^2\right )+e^{2 x} \left (15-6 x-3 x^2+2 x^3\right )+e^x \left (-90+42 x-24 x^2+2 x^3+6 x^4-4 x^5\right )+e^{e^2} \left (-90+24 x-18 x^2-4 x^3+4 x^4+e^x \left (30-6 x-6 x^2+2 x^3\right )\right )}{x^6} \, dx=\left (-2-\frac {3-e^{e^2}-e^x-x}{x^2}\right )^2 \left (-\frac {3}{x}+x\right ) \]
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Result contains higher order function than in optimal. Order 4 vs. order 3 in optimal.
Time = 0.58 (sec) , antiderivative size = 406, normalized size of antiderivative = 11.94, number of steps used = 47, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {14, 2230, 2208, 2209} \[ \int \frac {135-72 x+90 x^2-12 x^3-x^4+4 x^6+e^{2 e^2} \left (15-3 x^2\right )+e^{2 x} \left (15-6 x-3 x^2+2 x^3\right )+e^x \left (-90+42 x-24 x^2+2 x^3+6 x^4-4 x^5\right )+e^{e^2} \left (-90+24 x-18 x^2-4 x^3+4 x^4+e^x \left (30-6 x-6 x^2+2 x^3\right )\right )}{x^6} \, dx=-\left (4+e^{e^2}\right ) \operatorname {ExpIntegralEi}(x)+\left (1+e^{e^2}\right ) \operatorname {ExpIntegralEi}(x)+\frac {1}{4} \left (7-e^{e^2}\right ) \operatorname {ExpIntegralEi}(x)-\frac {1}{4} \left (3-e^{e^2}\right ) \operatorname {ExpIntegralEi}(x)+2 \operatorname {ExpIntegralEi}(x)-\frac {3 e^{2 x}}{x^5}-\frac {3 \left (3-e^{e^2}\right )^2}{x^5}+\frac {6 \left (3-e^{e^2}\right ) e^x}{x^5}-\frac {3 \left (7-e^{e^2}\right ) e^x}{2 x^4}+\frac {3 \left (3-e^{e^2}\right ) e^x}{2 x^4}+\frac {6 \left (3-e^{e^2}\right )}{x^4}+\frac {e^{2 x}}{x^3}-\frac {30-6 e^{e^2}-e^{2 e^2}}{x^3}+\frac {2 \left (4+e^{e^2}\right ) e^x}{x^3}-\frac {\left (7-e^{e^2}\right ) e^x}{2 x^3}+\frac {\left (3-e^{e^2}\right ) e^x}{2 x^3}+\frac {\left (4+e^{e^2}\right ) e^x}{x^2}+\frac {2 \left (3+e^{e^2}\right )}{x^2}-\frac {\left (1+e^{e^2}\right ) e^x}{x^2}-\frac {\left (7-e^{e^2}\right ) e^x}{4 x^2}+\frac {\left (3-e^{e^2}\right ) e^x}{4 x^2}+4 x-\frac {6 e^x}{x}+\frac {\left (4+e^{e^2}\right ) e^x}{x}-\frac {\left (1+e^{e^2}\right ) e^x}{x}-\frac {\left (7-e^{e^2}\right ) e^x}{4 x}+\frac {\left (3-e^{e^2}\right ) e^x}{4 x}+\frac {1-4 e^{e^2}}{x} \]
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Rule 14
Rule 2208
Rule 2209
Rule 2230
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {e^{2 x} \left (15-6 x-3 x^2+2 x^3\right )}{x^6}+\frac {2 e^x \left (-45 \left (1-\frac {e^{e^2}}{3}\right )+21 \left (1-\frac {e^{e^2}}{7}\right ) x-12 \left (1+\frac {e^{e^2}}{4}\right ) x^2+\left (1+e^{e^2}\right ) x^3+3 x^4-2 x^5\right )}{x^6}+\frac {135 \left (1+\frac {1}{9} e^{e^2} \left (-6+e^{e^2}\right )\right )-72 \left (1-\frac {e^{e^2}}{3}\right ) x+90 \left (1-\frac {1}{30} e^{e^2} \left (6+e^{e^2}\right )\right ) x^2-12 \left (1+\frac {e^{e^2}}{3}\right ) x^3-\left (1-4 e^{e^2}\right ) x^4+4 x^6}{x^6}\right ) \, dx \\ & = 2 \int \frac {e^x \left (-45 \left (1-\frac {e^{e^2}}{3}\right )+21 \left (1-\frac {e^{e^2}}{7}\right ) x-12 \left (1+\frac {e^{e^2}}{4}\right ) x^2+\left (1+e^{e^2}\right ) x^3+3 x^4-2 x^5\right )}{x^6} \, dx+\int \frac {e^{2 x} \left (15-6 x-3 x^2+2 x^3\right )}{x^6} \, dx+\int \frac {135 \left (1+\frac {1}{9} e^{e^2} \left (-6+e^{e^2}\right )\right )-72 \left (1-\frac {e^{e^2}}{3}\right ) x+90 \left (1-\frac {1}{30} e^{e^2} \left (6+e^{e^2}\right )\right ) x^2-12 \left (1+\frac {e^{e^2}}{3}\right ) x^3-\left (1-4 e^{e^2}\right ) x^4+4 x^6}{x^6} \, dx \\ & = 2 \int \left (\frac {15 e^x \left (-3+e^{e^2}\right )}{x^6}-\frac {3 e^x \left (-7+e^{e^2}\right )}{x^5}-\frac {3 e^x \left (4+e^{e^2}\right )}{x^4}+\frac {e^x \left (1+e^{e^2}\right )}{x^3}+\frac {3 e^x}{x^2}-\frac {2 e^x}{x}\right ) \, dx+\int \left (\frac {15 e^{2 x}}{x^6}-\frac {6 e^{2 x}}{x^5}-\frac {3 e^{2 x}}{x^4}+\frac {2 e^{2 x}}{x^3}\right ) \, dx+\int \left (4+\frac {15 \left (-3+e^{e^2}\right )^2}{x^6}+\frac {24 \left (-3+e^{e^2}\right )}{x^5}-\frac {3 \left (-30+6 e^{e^2}+e^{2 e^2}\right )}{x^4}-\frac {4 \left (3+e^{e^2}\right )}{x^3}+\frac {-1+4 e^{e^2}}{x^2}\right ) \, dx \\ & = -\frac {3 \left (3-e^{e^2}\right )^2}{x^5}+\frac {6 \left (3-e^{e^2}\right )}{x^4}-\frac {30-6 e^{e^2}-e^{2 e^2}}{x^3}+\frac {2 \left (3+e^{e^2}\right )}{x^2}+\frac {1-4 e^{e^2}}{x}+4 x+2 \int \frac {e^{2 x}}{x^3} \, dx-3 \int \frac {e^{2 x}}{x^4} \, dx-4 \int \frac {e^x}{x} \, dx-6 \int \frac {e^{2 x}}{x^5} \, dx+6 \int \frac {e^x}{x^2} \, dx+15 \int \frac {e^{2 x}}{x^6} \, dx-\left (30 \left (3-e^{e^2}\right )\right ) \int \frac {e^x}{x^6} \, dx+\left (6 \left (7-e^{e^2}\right )\right ) \int \frac {e^x}{x^5} \, dx+\left (2 \left (1+e^{e^2}\right )\right ) \int \frac {e^x}{x^3} \, dx-\left (6 \left (4+e^{e^2}\right )\right ) \int \frac {e^x}{x^4} \, dx \\ & = -\frac {3 e^{2 x}}{x^5}+\frac {6 e^x \left (3-e^{e^2}\right )}{x^5}-\frac {3 \left (3-e^{e^2}\right )^2}{x^5}+\frac {3 e^{2 x}}{2 x^4}+\frac {6 \left (3-e^{e^2}\right )}{x^4}-\frac {3 e^x \left (7-e^{e^2}\right )}{2 x^4}+\frac {e^{2 x}}{x^3}+\frac {2 e^x \left (4+e^{e^2}\right )}{x^3}-\frac {30-6 e^{e^2}-e^{2 e^2}}{x^3}-\frac {e^{2 x}}{x^2}-\frac {e^x \left (1+e^{e^2}\right )}{x^2}+\frac {2 \left (3+e^{e^2}\right )}{x^2}-\frac {6 e^x}{x}+\frac {1-4 e^{e^2}}{x}+4 x-4 \operatorname {ExpIntegralEi}(x)-2 \int \frac {e^{2 x}}{x^3} \, dx+2 \int \frac {e^{2 x}}{x^2} \, dx-3 \int \frac {e^{2 x}}{x^4} \, dx+6 \int \frac {e^{2 x}}{x^5} \, dx+6 \int \frac {e^x}{x} \, dx-\left (6 \left (3-e^{e^2}\right )\right ) \int \frac {e^x}{x^5} \, dx+\frac {1}{2} \left (3 \left (7-e^{e^2}\right )\right ) \int \frac {e^x}{x^4} \, dx+\left (1+e^{e^2}\right ) \int \frac {e^x}{x^2} \, dx-\left (2 \left (4+e^{e^2}\right )\right ) \int \frac {e^x}{x^3} \, dx \\ & = -\frac {3 e^{2 x}}{x^5}+\frac {6 e^x \left (3-e^{e^2}\right )}{x^5}-\frac {3 \left (3-e^{e^2}\right )^2}{x^5}+\frac {6 \left (3-e^{e^2}\right )}{x^4}+\frac {3 e^x \left (3-e^{e^2}\right )}{2 x^4}-\frac {3 e^x \left (7-e^{e^2}\right )}{2 x^4}+\frac {2 e^{2 x}}{x^3}-\frac {e^x \left (7-e^{e^2}\right )}{2 x^3}+\frac {2 e^x \left (4+e^{e^2}\right )}{x^3}-\frac {30-6 e^{e^2}-e^{2 e^2}}{x^3}-\frac {e^x \left (1+e^{e^2}\right )}{x^2}+\frac {2 \left (3+e^{e^2}\right )}{x^2}+\frac {e^x \left (4+e^{e^2}\right )}{x^2}-\frac {6 e^x}{x}-\frac {2 e^{2 x}}{x}+\frac {1-4 e^{e^2}}{x}-\frac {e^x \left (1+e^{e^2}\right )}{x}+4 x+2 \operatorname {ExpIntegralEi}(x)-2 \int \frac {e^{2 x}}{x^3} \, dx-2 \int \frac {e^{2 x}}{x^2} \, dx+3 \int \frac {e^{2 x}}{x^4} \, dx+4 \int \frac {e^{2 x}}{x} \, dx-\frac {1}{2} \left (3 \left (3-e^{e^2}\right )\right ) \int \frac {e^x}{x^4} \, dx+\frac {1}{2} \left (7-e^{e^2}\right ) \int \frac {e^x}{x^3} \, dx+\left (1+e^{e^2}\right ) \int \frac {e^x}{x} \, dx-\left (4+e^{e^2}\right ) \int \frac {e^x}{x^2} \, dx \\ & = -\frac {3 e^{2 x}}{x^5}+\frac {6 e^x \left (3-e^{e^2}\right )}{x^5}-\frac {3 \left (3-e^{e^2}\right )^2}{x^5}+\frac {6 \left (3-e^{e^2}\right )}{x^4}+\frac {3 e^x \left (3-e^{e^2}\right )}{2 x^4}-\frac {3 e^x \left (7-e^{e^2}\right )}{2 x^4}+\frac {e^{2 x}}{x^3}+\frac {e^x \left (3-e^{e^2}\right )}{2 x^3}-\frac {e^x \left (7-e^{e^2}\right )}{2 x^3}+\frac {2 e^x \left (4+e^{e^2}\right )}{x^3}-\frac {30-6 e^{e^2}-e^{2 e^2}}{x^3}+\frac {e^{2 x}}{x^2}-\frac {e^x \left (7-e^{e^2}\right )}{4 x^2}-\frac {e^x \left (1+e^{e^2}\right )}{x^2}+\frac {2 \left (3+e^{e^2}\right )}{x^2}+\frac {e^x \left (4+e^{e^2}\right )}{x^2}-\frac {6 e^x}{x}+\frac {1-4 e^{e^2}}{x}-\frac {e^x \left (1+e^{e^2}\right )}{x}+\frac {e^x \left (4+e^{e^2}\right )}{x}+4 x+2 \operatorname {ExpIntegralEi}(x)+\left (1+e^{e^2}\right ) \operatorname {ExpIntegralEi}(x)+4 \operatorname {ExpIntegralEi}(2 x)+2 \int \frac {e^{2 x}}{x^3} \, dx-2 \int \frac {e^{2 x}}{x^2} \, dx-4 \int \frac {e^{2 x}}{x} \, dx-\frac {1}{2} \left (3-e^{e^2}\right ) \int \frac {e^x}{x^3} \, dx+\frac {1}{4} \left (7-e^{e^2}\right ) \int \frac {e^x}{x^2} \, dx-\left (4+e^{e^2}\right ) \int \frac {e^x}{x} \, dx \\ & = -\frac {3 e^{2 x}}{x^5}+\frac {6 e^x \left (3-e^{e^2}\right )}{x^5}-\frac {3 \left (3-e^{e^2}\right )^2}{x^5}+\frac {6 \left (3-e^{e^2}\right )}{x^4}+\frac {3 e^x \left (3-e^{e^2}\right )}{2 x^4}-\frac {3 e^x \left (7-e^{e^2}\right )}{2 x^4}+\frac {e^{2 x}}{x^3}+\frac {e^x \left (3-e^{e^2}\right )}{2 x^3}-\frac {e^x \left (7-e^{e^2}\right )}{2 x^3}+\frac {2 e^x \left (4+e^{e^2}\right )}{x^3}-\frac {30-6 e^{e^2}-e^{2 e^2}}{x^3}+\frac {e^x \left (3-e^{e^2}\right )}{4 x^2}-\frac {e^x \left (7-e^{e^2}\right )}{4 x^2}-\frac {e^x \left (1+e^{e^2}\right )}{x^2}+\frac {2 \left (3+e^{e^2}\right )}{x^2}+\frac {e^x \left (4+e^{e^2}\right )}{x^2}-\frac {6 e^x}{x}+\frac {2 e^{2 x}}{x}+\frac {1-4 e^{e^2}}{x}-\frac {e^x \left (7-e^{e^2}\right )}{4 x}-\frac {e^x \left (1+e^{e^2}\right )}{x}+\frac {e^x \left (4+e^{e^2}\right )}{x}+4 x+2 \operatorname {ExpIntegralEi}(x)+\left (1+e^{e^2}\right ) \operatorname {ExpIntegralEi}(x)-\left (4+e^{e^2}\right ) \operatorname {ExpIntegralEi}(x)+2 \int \frac {e^{2 x}}{x^2} \, dx-4 \int \frac {e^{2 x}}{x} \, dx-\frac {1}{4} \left (3-e^{e^2}\right ) \int \frac {e^x}{x^2} \, dx+\frac {1}{4} \left (7-e^{e^2}\right ) \int \frac {e^x}{x} \, dx \\ & = -\frac {3 e^{2 x}}{x^5}+\frac {6 e^x \left (3-e^{e^2}\right )}{x^5}-\frac {3 \left (3-e^{e^2}\right )^2}{x^5}+\frac {6 \left (3-e^{e^2}\right )}{x^4}+\frac {3 e^x \left (3-e^{e^2}\right )}{2 x^4}-\frac {3 e^x \left (7-e^{e^2}\right )}{2 x^4}+\frac {e^{2 x}}{x^3}+\frac {e^x \left (3-e^{e^2}\right )}{2 x^3}-\frac {e^x \left (7-e^{e^2}\right )}{2 x^3}+\frac {2 e^x \left (4+e^{e^2}\right )}{x^3}-\frac {30-6 e^{e^2}-e^{2 e^2}}{x^3}+\frac {e^x \left (3-e^{e^2}\right )}{4 x^2}-\frac {e^x \left (7-e^{e^2}\right )}{4 x^2}-\frac {e^x \left (1+e^{e^2}\right )}{x^2}+\frac {2 \left (3+e^{e^2}\right )}{x^2}+\frac {e^x \left (4+e^{e^2}\right )}{x^2}-\frac {6 e^x}{x}+\frac {1-4 e^{e^2}}{x}+\frac {e^x \left (3-e^{e^2}\right )}{4 x}-\frac {e^x \left (7-e^{e^2}\right )}{4 x}-\frac {e^x \left (1+e^{e^2}\right )}{x}+\frac {e^x \left (4+e^{e^2}\right )}{x}+4 x+2 \operatorname {ExpIntegralEi}(x)+\frac {1}{4} \left (7-e^{e^2}\right ) \operatorname {ExpIntegralEi}(x)+\left (1+e^{e^2}\right ) \operatorname {ExpIntegralEi}(x)-\left (4+e^{e^2}\right ) \operatorname {ExpIntegralEi}(x)-4 \operatorname {ExpIntegralEi}(2 x)+4 \int \frac {e^{2 x}}{x} \, dx-\frac {1}{4} \left (3-e^{e^2}\right ) \int \frac {e^x}{x} \, dx \\ & = -\frac {3 e^{2 x}}{x^5}+\frac {6 e^x \left (3-e^{e^2}\right )}{x^5}-\frac {3 \left (3-e^{e^2}\right )^2}{x^5}+\frac {6 \left (3-e^{e^2}\right )}{x^4}+\frac {3 e^x \left (3-e^{e^2}\right )}{2 x^4}-\frac {3 e^x \left (7-e^{e^2}\right )}{2 x^4}+\frac {e^{2 x}}{x^3}+\frac {e^x \left (3-e^{e^2}\right )}{2 x^3}-\frac {e^x \left (7-e^{e^2}\right )}{2 x^3}+\frac {2 e^x \left (4+e^{e^2}\right )}{x^3}-\frac {30-6 e^{e^2}-e^{2 e^2}}{x^3}+\frac {e^x \left (3-e^{e^2}\right )}{4 x^2}-\frac {e^x \left (7-e^{e^2}\right )}{4 x^2}-\frac {e^x \left (1+e^{e^2}\right )}{x^2}+\frac {2 \left (3+e^{e^2}\right )}{x^2}+\frac {e^x \left (4+e^{e^2}\right )}{x^2}-\frac {6 e^x}{x}+\frac {1-4 e^{e^2}}{x}+\frac {e^x \left (3-e^{e^2}\right )}{4 x}-\frac {e^x \left (7-e^{e^2}\right )}{4 x}-\frac {e^x \left (1+e^{e^2}\right )}{x}+\frac {e^x \left (4+e^{e^2}\right )}{x}+4 x+2 \operatorname {ExpIntegralEi}(x)-\frac {1}{4} \left (3-e^{e^2}\right ) \operatorname {ExpIntegralEi}(x)+\frac {1}{4} \left (7-e^{e^2}\right ) \operatorname {ExpIntegralEi}(x)+\left (1+e^{e^2}\right ) \operatorname {ExpIntegralEi}(x)-\left (4+e^{e^2}\right ) \operatorname {ExpIntegralEi}(x) \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(113\) vs. \(2(34)=68\).
Time = 6.85 (sec) , antiderivative size = 113, normalized size of antiderivative = 3.32 \[ \int \frac {135-72 x+90 x^2-12 x^3-x^4+4 x^6+e^{2 e^2} \left (15-3 x^2\right )+e^{2 x} \left (15-6 x-3 x^2+2 x^3\right )+e^x \left (-90+42 x-24 x^2+2 x^3+6 x^4-4 x^5\right )+e^{e^2} \left (-90+24 x-18 x^2-4 x^3+4 x^4+e^x \left (30-6 x-6 x^2+2 x^3\right )\right )}{x^6} \, dx=\frac {-27+18 x-30 x^2+6 x^3+x^4+4 x^6+e^{2 e^2} \left (-3+x^2\right )+e^{2 x} \left (-3+x^2\right )+2 e^{e^2+x} \left (-3+x^2\right )+2 e^{e^2} \left (9-3 x+3 x^2+x^3-2 x^4\right )+2 e^x \left (9-3 x+3 x^2+x^3-2 x^4\right )}{x^5} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(119\) vs. \(2(31)=62\).
Time = 0.23 (sec) , antiderivative size = 120, normalized size of antiderivative = 3.53
method | result | size |
risch | \(4 x +\frac {\left (1-4 \,{\mathrm e}^{{\mathrm e}^{2}}\right ) x^{4}+\left (6+2 \,{\mathrm e}^{{\mathrm e}^{2}}\right ) x^{3}+\left ({\mathrm e}^{2 \,{\mathrm e}^{2}}+6 \,{\mathrm e}^{{\mathrm e}^{2}}-30\right ) x^{2}+\left (18-6 \,{\mathrm e}^{{\mathrm e}^{2}}\right ) x -3 \,{\mathrm e}^{2 \,{\mathrm e}^{2}}+18 \,{\mathrm e}^{{\mathrm e}^{2}}-27}{x^{5}}+\frac {\left (x^{2}-3\right ) {\mathrm e}^{2 x}}{x^{5}}+\frac {2 \left (-2 x^{4}+x^{2} {\mathrm e}^{{\mathrm e}^{2}}+x^{3}+3 x^{2}-3 \,{\mathrm e}^{{\mathrm e}^{2}}-3 x +9\right ) {\mathrm e}^{x}}{x^{5}}\) | \(120\) |
norman | \(\frac {\left (1-4 \,{\mathrm e}^{{\mathrm e}^{2}}\right ) x^{4}+\left (6+2 \,{\mathrm e}^{{\mathrm e}^{2}}\right ) x^{3}+\left (18-6 \,{\mathrm e}^{{\mathrm e}^{2}}\right ) x +\left (18-6 \,{\mathrm e}^{{\mathrm e}^{2}}\right ) {\mathrm e}^{x}+\left ({\mathrm e}^{2 \,{\mathrm e}^{2}}+6 \,{\mathrm e}^{{\mathrm e}^{2}}-30\right ) x^{2}+{\mathrm e}^{2 x} x^{2}+\left (6+2 \,{\mathrm e}^{{\mathrm e}^{2}}\right ) x^{2} {\mathrm e}^{x}+4 x^{6}-3 \,{\mathrm e}^{2 x}-6 \,{\mathrm e}^{x} x +2 \,{\mathrm e}^{x} x^{3}-4 \,{\mathrm e}^{x} x^{4}-3 \,{\mathrm e}^{2 \,{\mathrm e}^{2}}+18 \,{\mathrm e}^{{\mathrm e}^{2}}-27}{x^{5}}\) | \(127\) |
parallelrisch | \(\frac {4 x^{6}-4 \,{\mathrm e}^{x} x^{4}-4 \,{\mathrm e}^{{\mathrm e}^{2}} x^{4}+2 \,{\mathrm e}^{x} {\mathrm e}^{{\mathrm e}^{2}} x^{2}+2 \,{\mathrm e}^{x} x^{3}+2 x^{3} {\mathrm e}^{{\mathrm e}^{2}}+x^{4}+6 \,{\mathrm e}^{x} x^{2}+{\mathrm e}^{2 x} x^{2}+x^{2} {\mathrm e}^{2 \,{\mathrm e}^{2}}+6 x^{2} {\mathrm e}^{{\mathrm e}^{2}}+6 x^{3}-6 \,{\mathrm e}^{x} {\mathrm e}^{{\mathrm e}^{2}}-6 \,{\mathrm e}^{x} x -6 x \,{\mathrm e}^{{\mathrm e}^{2}}-30 x^{2}+18 \,{\mathrm e}^{x}-3 \,{\mathrm e}^{2 x}-3 \,{\mathrm e}^{2 \,{\mathrm e}^{2}}+18 \,{\mathrm e}^{{\mathrm e}^{2}}+18 x -27}{x^{5}}\) | \(140\) |
parts | \(\frac {{\mathrm e}^{2 x}}{x^{3}}-\frac {3 \,{\mathrm e}^{2 x}}{x^{5}}+4 x +\frac {1-4 \,{\mathrm e}^{{\mathrm e}^{2}}}{x}+\frac {-15 \,{\mathrm e}^{2 \,{\mathrm e}^{2}}+90 \,{\mathrm e}^{{\mathrm e}^{2}}-135}{5 x^{5}}+\frac {12+4 \,{\mathrm e}^{{\mathrm e}^{2}}}{2 x^{2}}+\frac {72-24 \,{\mathrm e}^{{\mathrm e}^{2}}}{4 x^{4}}+\frac {3 \,{\mathrm e}^{2 \,{\mathrm e}^{2}}+18 \,{\mathrm e}^{{\mathrm e}^{2}}-90}{3 x^{3}}+\frac {2 \,{\mathrm e}^{x}}{x^{2}}-\frac {4 \,{\mathrm e}^{x}}{x}+2 \,{\mathrm e}^{{\mathrm e}^{2}} \left (-\frac {{\mathrm e}^{x}}{2 x^{2}}-\frac {{\mathrm e}^{x}}{2 x}-\frac {\operatorname {Ei}_{1}\left (-x \right )}{2}\right )+\frac {18 \,{\mathrm e}^{x}}{x^{5}}-\frac {6 \,{\mathrm e}^{x}}{x^{4}}+\frac {6 \,{\mathrm e}^{x}}{x^{3}}+30 \,{\mathrm e}^{{\mathrm e}^{2}} \left (-\frac {{\mathrm e}^{x}}{5 x^{5}}-\frac {{\mathrm e}^{x}}{20 x^{4}}-\frac {{\mathrm e}^{x}}{60 x^{3}}-\frac {{\mathrm e}^{x}}{120 x^{2}}-\frac {{\mathrm e}^{x}}{120 x}-\frac {\operatorname {Ei}_{1}\left (-x \right )}{120}\right )-6 \,{\mathrm e}^{{\mathrm e}^{2}} \left (-\frac {{\mathrm e}^{x}}{4 x^{4}}-\frac {{\mathrm e}^{x}}{12 x^{3}}-\frac {{\mathrm e}^{x}}{24 x^{2}}-\frac {{\mathrm e}^{x}}{24 x}-\frac {\operatorname {Ei}_{1}\left (-x \right )}{24}\right )-6 \,{\mathrm e}^{{\mathrm e}^{2}} \left (-\frac {{\mathrm e}^{x}}{3 x^{3}}-\frac {{\mathrm e}^{x}}{6 x^{2}}-\frac {{\mathrm e}^{x}}{6 x}-\frac {\operatorname {Ei}_{1}\left (-x \right )}{6}\right )\) | \(280\) |
default | \(4 x -\frac {27}{x^{5}}+\frac {18}{x^{4}}-\frac {30}{x^{3}}+\frac {6}{x^{2}}+\frac {1}{x}+\frac {18 \,{\mathrm e}^{x}}{x^{5}}-\frac {6 \,{\mathrm e}^{x}}{x^{4}}+\frac {6 \,{\mathrm e}^{x}}{x^{3}}+\frac {2 \,{\mathrm e}^{x}}{x^{2}}-\frac {4 \,{\mathrm e}^{x}}{x}+\frac {18 \,{\mathrm e}^{{\mathrm e}^{2}}}{x^{5}}-\frac {3 \,{\mathrm e}^{2 \,{\mathrm e}^{2}}}{x^{5}}-\frac {6 \,{\mathrm e}^{{\mathrm e}^{2}}}{x^{4}}+\frac {6 \,{\mathrm e}^{{\mathrm e}^{2}}}{x^{3}}+\frac {2 \,{\mathrm e}^{{\mathrm e}^{2}}}{x^{2}}-\frac {3 \,{\mathrm e}^{2 x}}{x^{5}}+\frac {{\mathrm e}^{2 x}}{x^{3}}-\frac {4 \,{\mathrm e}^{{\mathrm e}^{2}}}{x}+\frac {{\mathrm e}^{2 \,{\mathrm e}^{2}}}{x^{3}}+30 \,{\mathrm e}^{{\mathrm e}^{2}} \left (-\frac {{\mathrm e}^{x}}{5 x^{5}}-\frac {{\mathrm e}^{x}}{20 x^{4}}-\frac {{\mathrm e}^{x}}{60 x^{3}}-\frac {{\mathrm e}^{x}}{120 x^{2}}-\frac {{\mathrm e}^{x}}{120 x}-\frac {\operatorname {Ei}_{1}\left (-x \right )}{120}\right )-6 \,{\mathrm e}^{{\mathrm e}^{2}} \left (-\frac {{\mathrm e}^{x}}{4 x^{4}}-\frac {{\mathrm e}^{x}}{12 x^{3}}-\frac {{\mathrm e}^{x}}{24 x^{2}}-\frac {{\mathrm e}^{x}}{24 x}-\frac {\operatorname {Ei}_{1}\left (-x \right )}{24}\right )-6 \,{\mathrm e}^{{\mathrm e}^{2}} \left (-\frac {{\mathrm e}^{x}}{3 x^{3}}-\frac {{\mathrm e}^{x}}{6 x^{2}}-\frac {{\mathrm e}^{x}}{6 x}-\frac {\operatorname {Ei}_{1}\left (-x \right )}{6}\right )+2 \,{\mathrm e}^{{\mathrm e}^{2}} \left (-\frac {{\mathrm e}^{x}}{2 x^{2}}-\frac {{\mathrm e}^{x}}{2 x}-\frac {\operatorname {Ei}_{1}\left (-x \right )}{2}\right )\) | \(289\) |
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Leaf count of result is larger than twice the leaf count of optimal. 106 vs. \(2 (24) = 48\).
Time = 0.26 (sec) , antiderivative size = 106, normalized size of antiderivative = 3.12 \[ \int \frac {135-72 x+90 x^2-12 x^3-x^4+4 x^6+e^{2 e^2} \left (15-3 x^2\right )+e^{2 x} \left (15-6 x-3 x^2+2 x^3\right )+e^x \left (-90+42 x-24 x^2+2 x^3+6 x^4-4 x^5\right )+e^{e^2} \left (-90+24 x-18 x^2-4 x^3+4 x^4+e^x \left (30-6 x-6 x^2+2 x^3\right )\right )}{x^6} \, dx=\frac {4 \, x^{6} + x^{4} + 6 \, x^{3} - 30 \, x^{2} + {\left (x^{2} - 3\right )} e^{\left (2 \, x\right )} - 2 \, {\left (2 \, x^{4} - x^{3} - 3 \, x^{2} + 3 \, x - 9\right )} e^{x} + {\left (x^{2} - 3\right )} e^{\left (2 \, e^{2}\right )} - 2 \, {\left (2 \, x^{4} - x^{3} - 3 \, x^{2} - {\left (x^{2} - 3\right )} e^{x} + 3 \, x - 9\right )} e^{\left (e^{2}\right )} + 18 \, x - 27}{x^{5}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 141 vs. \(2 (24) = 48\).
Time = 1.45 (sec) , antiderivative size = 141, normalized size of antiderivative = 4.15 \[ \int \frac {135-72 x+90 x^2-12 x^3-x^4+4 x^6+e^{2 e^2} \left (15-3 x^2\right )+e^{2 x} \left (15-6 x-3 x^2+2 x^3\right )+e^x \left (-90+42 x-24 x^2+2 x^3+6 x^4-4 x^5\right )+e^{e^2} \left (-90+24 x-18 x^2-4 x^3+4 x^4+e^x \left (30-6 x-6 x^2+2 x^3\right )\right )}{x^6} \, dx=4 x + \frac {x^{4} \cdot \left (1 - 4 e^{e^{2}}\right ) + x^{3} \cdot \left (6 + 2 e^{e^{2}}\right ) + x^{2} \left (-30 + 6 e^{e^{2}} + e^{2 e^{2}}\right ) + x \left (18 - 6 e^{e^{2}}\right ) - 3 e^{2 e^{2}} - 27 + 18 e^{e^{2}}}{x^{5}} + \frac {\left (x^{7} - 3 x^{5}\right ) e^{2 x} + \left (- 4 x^{9} + 2 x^{8} + 6 x^{7} + 2 x^{7} e^{e^{2}} - 6 x^{6} - 6 x^{5} e^{e^{2}} + 18 x^{5}\right ) e^{x}}{x^{10}} \]
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Result contains higher order function than in optimal. Order 4 vs. order 3.
Time = 0.27 (sec) , antiderivative size = 193, normalized size of antiderivative = 5.68 \[ \int \frac {135-72 x+90 x^2-12 x^3-x^4+4 x^6+e^{2 e^2} \left (15-3 x^2\right )+e^{2 x} \left (15-6 x-3 x^2+2 x^3\right )+e^x \left (-90+42 x-24 x^2+2 x^3+6 x^4-4 x^5\right )+e^{e^2} \left (-90+24 x-18 x^2-4 x^3+4 x^4+e^x \left (30-6 x-6 x^2+2 x^3\right )\right )}{x^6} \, dx=-2 \, e^{\left (e^{2}\right )} \Gamma \left (-2, -x\right ) - 6 \, e^{\left (e^{2}\right )} \Gamma \left (-3, -x\right ) + 6 \, e^{\left (e^{2}\right )} \Gamma \left (-4, -x\right ) + 30 \, e^{\left (e^{2}\right )} \Gamma \left (-5, -x\right ) + 4 \, x - \frac {4 \, e^{\left (e^{2}\right )}}{x} + \frac {1}{x} + \frac {2 \, e^{\left (e^{2}\right )}}{x^{2}} + \frac {6}{x^{2}} + \frac {e^{\left (2 \, e^{2}\right )}}{x^{3}} + \frac {6 \, e^{\left (e^{2}\right )}}{x^{3}} - \frac {30}{x^{3}} - \frac {6 \, e^{\left (e^{2}\right )}}{x^{4}} + \frac {18}{x^{4}} - \frac {3 \, e^{\left (2 \, e^{2}\right )}}{x^{5}} + \frac {18 \, e^{\left (e^{2}\right )}}{x^{5}} - \frac {27}{x^{5}} - 4 \, {\rm Ei}\left (x\right ) + 6 \, \Gamma \left (-1, -x\right ) - 2 \, \Gamma \left (-2, -x\right ) - 8 \, \Gamma \left (-2, -2 \, x\right ) - 24 \, \Gamma \left (-3, -x\right ) - 24 \, \Gamma \left (-3, -2 \, x\right ) - 42 \, \Gamma \left (-4, -x\right ) + 96 \, \Gamma \left (-4, -2 \, x\right ) - 90 \, \Gamma \left (-5, -x\right ) + 480 \, \Gamma \left (-5, -2 \, x\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 139 vs. \(2 (24) = 48\).
Time = 0.28 (sec) , antiderivative size = 139, normalized size of antiderivative = 4.09 \[ \int \frac {135-72 x+90 x^2-12 x^3-x^4+4 x^6+e^{2 e^2} \left (15-3 x^2\right )+e^{2 x} \left (15-6 x-3 x^2+2 x^3\right )+e^x \left (-90+42 x-24 x^2+2 x^3+6 x^4-4 x^5\right )+e^{e^2} \left (-90+24 x-18 x^2-4 x^3+4 x^4+e^x \left (30-6 x-6 x^2+2 x^3\right )\right )}{x^6} \, dx=\frac {4 \, x^{6} - 4 \, x^{4} e^{x} - 4 \, x^{4} e^{\left (e^{2}\right )} + x^{4} + 2 \, x^{3} e^{x} + 2 \, x^{3} e^{\left (e^{2}\right )} + 6 \, x^{3} + x^{2} e^{\left (2 \, x\right )} + 2 \, x^{2} e^{\left (x + e^{2}\right )} + 6 \, x^{2} e^{x} + x^{2} e^{\left (2 \, e^{2}\right )} + 6 \, x^{2} e^{\left (e^{2}\right )} - 30 \, x^{2} - 6 \, x e^{x} - 6 \, x e^{\left (e^{2}\right )} + 18 \, x - 3 \, e^{\left (2 \, x\right )} - 6 \, e^{\left (x + e^{2}\right )} + 18 \, e^{x} - 3 \, e^{\left (2 \, e^{2}\right )} + 18 \, e^{\left (e^{2}\right )} - 27}{x^{5}} \]
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Time = 11.60 (sec) , antiderivative size = 96, normalized size of antiderivative = 2.82 \[ \int \frac {135-72 x+90 x^2-12 x^3-x^4+4 x^6+e^{2 e^2} \left (15-3 x^2\right )+e^{2 x} \left (15-6 x-3 x^2+2 x^3\right )+e^x \left (-90+42 x-24 x^2+2 x^3+6 x^4-4 x^5\right )+e^{e^2} \left (-90+24 x-18 x^2-4 x^3+4 x^4+e^x \left (30-6 x-6 x^2+2 x^3\right )\right )}{x^6} \, dx=4\,x+\frac {{\mathrm {e}}^{2\,{\mathrm {e}}^2}+{\mathrm {e}}^{2\,x}+2\,{\mathrm {e}}^{x+{\mathrm {e}}^2}+6\,{\mathrm {e}}^{{\mathrm {e}}^2}+6\,{\mathrm {e}}^x-30}{x^3}-\frac {3\,{\left ({\mathrm {e}}^{{\mathrm {e}}^2}+{\mathrm {e}}^x-3\right )}^2}{x^5}-\frac {4\,{\mathrm {e}}^{{\mathrm {e}}^2}+4\,{\mathrm {e}}^x-1}{x}+\frac {2\,{\mathrm {e}}^{{\mathrm {e}}^2}+2\,{\mathrm {e}}^x+6}{x^2}-\frac {6\,{\mathrm {e}}^{{\mathrm {e}}^2}+6\,{\mathrm {e}}^x-18}{x^4} \]
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