Integrand size = 180, antiderivative size = 25 \[ \int \left (324 x^3+e^{9 e^{e^{e^x}}+3 x} \left (-750000 x^3-562500 x^4-1687500 e^{e^{e^x}+e^x+x} x^4\right )+e^{3 e^{e^{e^x}}+x} \left (-10800 x^3-2700 x^4-8100 e^{e^{e^x}+e^x+x} x^4\right )+e^{6 e^{e^{e^x}}+2 x} \left (135000 x^3+67500 x^4+202500 e^{e^{e^x}+e^x+x} x^4\right )+e^{12 e^{e^{e^x}}+4 x} \left (1562500 x^3+1562500 x^4+4687500 e^{e^{e^x}+e^x+x} x^4\right )\right ) \, dx=\left (-x+\left (4-25 e^{3 e^{e^{e^x}}+x}\right ) x\right )^4 \]
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Leaf count is larger than twice the leaf count of optimal. \(228\) vs. \(2(25)=50\).
Time = 0.45 (sec) , antiderivative size = 228, normalized size of antiderivative = 9.12, number of steps used = 5, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.006, Rules used = {2326} \[ \int \left (324 x^3+e^{9 e^{e^{e^x}}+3 x} \left (-750000 x^3-562500 x^4-1687500 e^{e^{e^x}+e^x+x} x^4\right )+e^{3 e^{e^{e^x}}+x} \left (-10800 x^3-2700 x^4-8100 e^{e^{e^x}+e^x+x} x^4\right )+e^{6 e^{e^{e^x}}+2 x} \left (135000 x^3+67500 x^4+202500 e^{e^{e^x}+e^x+x} x^4\right )+e^{12 e^{e^{e^x}}+4 x} \left (1562500 x^3+1562500 x^4+4687500 e^{e^{e^x}+e^x+x} x^4\right )\right ) \, dx=81 x^4-\frac {2700 e^{x+3 e^{e^{e^x}}} \left (3 e^{x+e^{e^x}+e^x} x^4+x^4\right )}{3 e^{x+e^{e^x}+e^x}+1}+\frac {33750 e^{2 x+6 e^{e^{e^x}}} \left (3 e^{x+e^{e^x}+e^x} x^4+x^4\right )}{3 e^{x+e^{e^x}+e^x}+1}-\frac {187500 e^{3 x+9 e^{e^{e^x}}} \left (3 e^{x+e^{e^x}+e^x} x^4+x^4\right )}{3 e^{x+e^{e^x}+e^x}+1}+\frac {390625 e^{4 x+12 e^{e^{e^x}}} \left (3 e^{x+e^{e^x}+e^x} x^4+x^4\right )}{3 e^{x+e^{e^x}+e^x}+1} \]
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Rule 2326
Rubi steps \begin{align*} \text {integral}& = 81 x^4+\int e^{9 e^{e^{e^x}}+3 x} \left (-750000 x^3-562500 x^4-1687500 e^{e^{e^x}+e^x+x} x^4\right ) \, dx+\int e^{3 e^{e^{e^x}}+x} \left (-10800 x^3-2700 x^4-8100 e^{e^{e^x}+e^x+x} x^4\right ) \, dx+\int e^{6 e^{e^{e^x}}+2 x} \left (135000 x^3+67500 x^4+202500 e^{e^{e^x}+e^x+x} x^4\right ) \, dx+\int e^{12 e^{e^{e^x}}+4 x} \left (1562500 x^3+1562500 x^4+4687500 e^{e^{e^x}+e^x+x} x^4\right ) \, dx \\ & = 81 x^4-\frac {2700 e^{3 e^{e^{e^x}}+x} \left (x^4+3 e^{e^{e^x}+e^x+x} x^4\right )}{1+3 e^{e^{e^x}+e^x+x}}+\frac {33750 e^{6 e^{e^{e^x}}+2 x} \left (x^4+3 e^{e^{e^x}+e^x+x} x^4\right )}{1+3 e^{e^{e^x}+e^x+x}}-\frac {187500 e^{9 e^{e^{e^x}}+3 x} \left (x^4+3 e^{e^{e^x}+e^x+x} x^4\right )}{1+3 e^{e^{e^x}+e^x+x}}+\frac {390625 e^{12 e^{e^{e^x}}+4 x} \left (x^4+3 e^{e^{e^x}+e^x+x} x^4\right )}{1+3 e^{e^{e^x}+e^x+x}} \\ \end{align*}
Time = 0.91 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.92 \[ \int \left (324 x^3+e^{9 e^{e^{e^x}}+3 x} \left (-750000 x^3-562500 x^4-1687500 e^{e^{e^x}+e^x+x} x^4\right )+e^{3 e^{e^{e^x}}+x} \left (-10800 x^3-2700 x^4-8100 e^{e^{e^x}+e^x+x} x^4\right )+e^{6 e^{e^{e^x}}+2 x} \left (135000 x^3+67500 x^4+202500 e^{e^{e^x}+e^x+x} x^4\right )+e^{12 e^{e^{e^x}}+4 x} \left (1562500 x^3+1562500 x^4+4687500 e^{e^{e^x}+e^x+x} x^4\right )\right ) \, dx=\left (3-25 e^{3 e^{e^{e^x}}+x}\right )^4 x^4 \]
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Leaf count of result is larger than twice the leaf count of optimal. \(68\) vs. \(2(21)=42\).
Time = 6.22 (sec) , antiderivative size = 69, normalized size of antiderivative = 2.76
method | result | size |
risch | \(390625 \,{\mathrm e}^{12 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}}+4 x} x^{4}-187500 \,{\mathrm e}^{9 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}}+3 x} x^{4}+33750 \,{\mathrm e}^{6 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}}+2 x} x^{4}-2700 \,{\mathrm e}^{3 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}}+x} x^{4}+81 x^{4}\) | \(69\) |
parallelrisch | \(390625 \,{\mathrm e}^{12 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}}+4 x} x^{4}-187500 \,{\mathrm e}^{9 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}}+3 x} x^{4}+33750 \,{\mathrm e}^{6 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}}+2 x} x^{4}-2700 \,{\mathrm e}^{3 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}}+x} x^{4}+81 x^{4}\) | \(69\) |
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Leaf count of result is larger than twice the leaf count of optimal. 145 vs. \(2 (19) = 38\).
Time = 0.24 (sec) , antiderivative size = 145, normalized size of antiderivative = 5.80 \[ \int \left (324 x^3+e^{9 e^{e^{e^x}}+3 x} \left (-750000 x^3-562500 x^4-1687500 e^{e^{e^x}+e^x+x} x^4\right )+e^{3 e^{e^{e^x}}+x} \left (-10800 x^3-2700 x^4-8100 e^{e^{e^x}+e^x+x} x^4\right )+e^{6 e^{e^{e^x}}+2 x} \left (135000 x^3+67500 x^4+202500 e^{e^{e^x}+e^x+x} x^4\right )+e^{12 e^{e^{e^x}}+4 x} \left (1562500 x^3+1562500 x^4+4687500 e^{e^{e^x}+e^x+x} x^4\right )\right ) \, dx=390625 \, x^{4} e^{\left (4 \, {\left (x e^{\left (x + e^{x}\right )} + 3 \, e^{\left (x + e^{x} + e^{\left (e^{x}\right )}\right )}\right )} e^{\left (-x - e^{x}\right )}\right )} - 187500 \, x^{4} e^{\left (3 \, {\left (x e^{\left (x + e^{x}\right )} + 3 \, e^{\left (x + e^{x} + e^{\left (e^{x}\right )}\right )}\right )} e^{\left (-x - e^{x}\right )}\right )} + 33750 \, x^{4} e^{\left (2 \, {\left (x e^{\left (x + e^{x}\right )} + 3 \, e^{\left (x + e^{x} + e^{\left (e^{x}\right )}\right )}\right )} e^{\left (-x - e^{x}\right )}\right )} - 2700 \, x^{4} e^{\left ({\left (x e^{\left (x + e^{x}\right )} + 3 \, e^{\left (x + e^{x} + e^{\left (e^{x}\right )}\right )}\right )} e^{\left (-x - e^{x}\right )}\right )} + 81 \, x^{4} \]
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Leaf count of result is larger than twice the leaf count of optimal. 76 vs. \(2 (19) = 38\).
Time = 4.26 (sec) , antiderivative size = 76, normalized size of antiderivative = 3.04 \[ \int \left (324 x^3+e^{9 e^{e^{e^x}}+3 x} \left (-750000 x^3-562500 x^4-1687500 e^{e^{e^x}+e^x+x} x^4\right )+e^{3 e^{e^{e^x}}+x} \left (-10800 x^3-2700 x^4-8100 e^{e^{e^x}+e^x+x} x^4\right )+e^{6 e^{e^{e^x}}+2 x} \left (135000 x^3+67500 x^4+202500 e^{e^{e^x}+e^x+x} x^4\right )+e^{12 e^{e^{e^x}}+4 x} \left (1562500 x^3+1562500 x^4+4687500 e^{e^{e^x}+e^x+x} x^4\right )\right ) \, dx=- 2700 x^{4} e^{x + 3 e^{e^{e^{x}}}} + 33750 x^{4} e^{2 x + 6 e^{e^{e^{x}}}} - 187500 x^{4} e^{3 x + 9 e^{e^{e^{x}}}} + 390625 x^{4} e^{4 x + 12 e^{e^{e^{x}}}} + 81 x^{4} \]
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Leaf count of result is larger than twice the leaf count of optimal. 68 vs. \(2 (19) = 38\).
Time = 0.29 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.72 \[ \int \left (324 x^3+e^{9 e^{e^{e^x}}+3 x} \left (-750000 x^3-562500 x^4-1687500 e^{e^{e^x}+e^x+x} x^4\right )+e^{3 e^{e^{e^x}}+x} \left (-10800 x^3-2700 x^4-8100 e^{e^{e^x}+e^x+x} x^4\right )+e^{6 e^{e^{e^x}}+2 x} \left (135000 x^3+67500 x^4+202500 e^{e^{e^x}+e^x+x} x^4\right )+e^{12 e^{e^{e^x}}+4 x} \left (1562500 x^3+1562500 x^4+4687500 e^{e^{e^x}+e^x+x} x^4\right )\right ) \, dx=390625 \, x^{4} e^{\left (4 \, x + 12 \, e^{\left (e^{\left (e^{x}\right )}\right )}\right )} - 187500 \, x^{4} e^{\left (3 \, x + 9 \, e^{\left (e^{\left (e^{x}\right )}\right )}\right )} + 33750 \, x^{4} e^{\left (2 \, x + 6 \, e^{\left (e^{\left (e^{x}\right )}\right )}\right )} - 2700 \, x^{4} e^{\left (x + 3 \, e^{\left (e^{\left (e^{x}\right )}\right )}\right )} + 81 \, x^{4} \]
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\[ \int \left (324 x^3+e^{9 e^{e^{e^x}}+3 x} \left (-750000 x^3-562500 x^4-1687500 e^{e^{e^x}+e^x+x} x^4\right )+e^{3 e^{e^{e^x}}+x} \left (-10800 x^3-2700 x^4-8100 e^{e^{e^x}+e^x+x} x^4\right )+e^{6 e^{e^{e^x}}+2 x} \left (135000 x^3+67500 x^4+202500 e^{e^{e^x}+e^x+x} x^4\right )+e^{12 e^{e^{e^x}}+4 x} \left (1562500 x^3+1562500 x^4+4687500 e^{e^{e^x}+e^x+x} x^4\right )\right ) \, dx=\int { 324 \, x^{3} + 1562500 \, {\left (3 \, x^{4} e^{\left (x + e^{x} + e^{\left (e^{x}\right )}\right )} + x^{4} + x^{3}\right )} e^{\left (4 \, x + 12 \, e^{\left (e^{\left (e^{x}\right )}\right )}\right )} - 187500 \, {\left (9 \, x^{4} e^{\left (x + e^{x} + e^{\left (e^{x}\right )}\right )} + 3 \, x^{4} + 4 \, x^{3}\right )} e^{\left (3 \, x + 9 \, e^{\left (e^{\left (e^{x}\right )}\right )}\right )} + 67500 \, {\left (3 \, x^{4} e^{\left (x + e^{x} + e^{\left (e^{x}\right )}\right )} + x^{4} + 2 \, x^{3}\right )} e^{\left (2 \, x + 6 \, e^{\left (e^{\left (e^{x}\right )}\right )}\right )} - 2700 \, {\left (3 \, x^{4} e^{\left (x + e^{x} + e^{\left (e^{x}\right )}\right )} + x^{4} + 4 \, x^{3}\right )} e^{\left (x + 3 \, e^{\left (e^{\left (e^{x}\right )}\right )}\right )} \,d x } \]
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Time = 0.42 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.72 \[ \int \left (324 x^3+e^{9 e^{e^{e^x}}+3 x} \left (-750000 x^3-562500 x^4-1687500 e^{e^{e^x}+e^x+x} x^4\right )+e^{3 e^{e^{e^x}}+x} \left (-10800 x^3-2700 x^4-8100 e^{e^{e^x}+e^x+x} x^4\right )+e^{6 e^{e^{e^x}}+2 x} \left (135000 x^3+67500 x^4+202500 e^{e^{e^x}+e^x+x} x^4\right )+e^{12 e^{e^{e^x}}+4 x} \left (1562500 x^3+1562500 x^4+4687500 e^{e^{e^x}+e^x+x} x^4\right )\right ) \, dx=81\,x^4-2700\,x^4\,{\mathrm {e}}^{x+3\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}}}+33750\,x^4\,{\mathrm {e}}^{2\,x+6\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}}}-187500\,x^4\,{\mathrm {e}}^{3\,x+9\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}}}+390625\,x^4\,{\mathrm {e}}^{4\,x+12\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}}} \]
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