Integrand size = 124, antiderivative size = 28 \[ \int \frac {e^{e^{e^x}} \left (30 x-15 x^2+e^x \left (-15-5 x+5 x^2\right )+e^{e^x} \left (e^{2 x} \left (15 x-5 x^2\right )+e^x \left (-15 x^2+5 x^3\right )\right )\right )}{9 x^4-6 x^5+x^6+e^{2 x} \left (9 x^2-6 x^3+x^4\right )+e^x \left (-18 x^3+12 x^4-2 x^5\right )} \, dx=\frac {5 e^{e^{e^x}}}{(3-x) \left (e^x-x\right ) x} \]
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Leaf count is larger than twice the leaf count of optimal. \(100\) vs. \(2(28)=56\).
Time = 0.17 (sec) , antiderivative size = 100, normalized size of antiderivative = 3.57, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.008, Rules used = {2326} \[ \int \frac {e^{e^{e^x}} \left (30 x-15 x^2+e^x \left (-15-5 x+5 x^2\right )+e^{e^x} \left (e^{2 x} \left (15 x-5 x^2\right )+e^x \left (-15 x^2+5 x^3\right )\right )\right )}{9 x^4-6 x^5+x^6+e^{2 x} \left (9 x^2-6 x^3+x^4\right )+e^x \left (-18 x^3+12 x^4-2 x^5\right )} \, dx=\frac {5 e^{e^{e^x}-x} \left (e^{2 x} \left (3 x-x^2\right )-e^x \left (3 x^2-x^3\right )\right )}{x^6-6 x^5+9 x^4-2 e^x \left (x^5-6 x^4+9 x^3\right )+e^{2 x} \left (x^4-6 x^3+9 x^2\right )} \]
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Rule 2326
Rubi steps \begin{align*} \text {integral}& = \frac {5 e^{e^{e^x}-x} \left (e^{2 x} \left (3 x-x^2\right )-e^x \left (3 x^2-x^3\right )\right )}{9 x^4-6 x^5+x^6+e^{2 x} \left (9 x^2-6 x^3+x^4\right )-2 e^x \left (9 x^3-6 x^4+x^5\right )} \\ \end{align*}
Time = 0.17 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.93 \[ \int \frac {e^{e^{e^x}} \left (30 x-15 x^2+e^x \left (-15-5 x+5 x^2\right )+e^{e^x} \left (e^{2 x} \left (15 x-5 x^2\right )+e^x \left (-15 x^2+5 x^3\right )\right )\right )}{9 x^4-6 x^5+x^6+e^{2 x} \left (9 x^2-6 x^3+x^4\right )+e^x \left (-18 x^3+12 x^4-2 x^5\right )} \, dx=-\frac {5 e^{e^{e^x}}}{\left (e^x-x\right ) (-3+x) x} \]
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Time = 1.85 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.00
method | result | size |
risch | \(\frac {5 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}}}{x \left (x^{2}-{\mathrm e}^{x} x -3 x +3 \,{\mathrm e}^{x}\right )}\) | \(28\) |
parallelrisch | \(\frac {5 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}}}{x \left (x^{2}-{\mathrm e}^{x} x -3 x +3 \,{\mathrm e}^{x}\right )}\) | \(28\) |
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none
Time = 0.26 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.00 \[ \int \frac {e^{e^{e^x}} \left (30 x-15 x^2+e^x \left (-15-5 x+5 x^2\right )+e^{e^x} \left (e^{2 x} \left (15 x-5 x^2\right )+e^x \left (-15 x^2+5 x^3\right )\right )\right )}{9 x^4-6 x^5+x^6+e^{2 x} \left (9 x^2-6 x^3+x^4\right )+e^x \left (-18 x^3+12 x^4-2 x^5\right )} \, dx=\frac {5 \, e^{\left (e^{\left (e^{x}\right )}\right )}}{x^{3} - 3 \, x^{2} - {\left (x^{2} - 3 \, x\right )} e^{x}} \]
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Time = 0.15 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.04 \[ \int \frac {e^{e^{e^x}} \left (30 x-15 x^2+e^x \left (-15-5 x+5 x^2\right )+e^{e^x} \left (e^{2 x} \left (15 x-5 x^2\right )+e^x \left (-15 x^2+5 x^3\right )\right )\right )}{9 x^4-6 x^5+x^6+e^{2 x} \left (9 x^2-6 x^3+x^4\right )+e^x \left (-18 x^3+12 x^4-2 x^5\right )} \, dx=\frac {5 e^{e^{e^{x}}}}{x^{3} - x^{2} e^{x} - 3 x^{2} + 3 x e^{x}} \]
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Time = 0.27 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.00 \[ \int \frac {e^{e^{e^x}} \left (30 x-15 x^2+e^x \left (-15-5 x+5 x^2\right )+e^{e^x} \left (e^{2 x} \left (15 x-5 x^2\right )+e^x \left (-15 x^2+5 x^3\right )\right )\right )}{9 x^4-6 x^5+x^6+e^{2 x} \left (9 x^2-6 x^3+x^4\right )+e^x \left (-18 x^3+12 x^4-2 x^5\right )} \, dx=\frac {5 \, e^{\left (e^{\left (e^{x}\right )}\right )}}{x^{3} - 3 \, x^{2} - {\left (x^{2} - 3 \, x\right )} e^{x}} \]
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\[ \int \frac {e^{e^{e^x}} \left (30 x-15 x^2+e^x \left (-15-5 x+5 x^2\right )+e^{e^x} \left (e^{2 x} \left (15 x-5 x^2\right )+e^x \left (-15 x^2+5 x^3\right )\right )\right )}{9 x^4-6 x^5+x^6+e^{2 x} \left (9 x^2-6 x^3+x^4\right )+e^x \left (-18 x^3+12 x^4-2 x^5\right )} \, dx=\int { -\frac {5 \, {\left (3 \, x^{2} - {\left (x^{2} - x - 3\right )} e^{x} + {\left ({\left (x^{2} - 3 \, x\right )} e^{\left (2 \, x\right )} - {\left (x^{3} - 3 \, x^{2}\right )} e^{x}\right )} e^{\left (e^{x}\right )} - 6 \, x\right )} e^{\left (e^{\left (e^{x}\right )}\right )}}{x^{6} - 6 \, x^{5} + 9 \, x^{4} + {\left (x^{4} - 6 \, x^{3} + 9 \, x^{2}\right )} e^{\left (2 \, x\right )} - 2 \, {\left (x^{5} - 6 \, x^{4} + 9 \, x^{3}\right )} e^{x}} \,d x } \]
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Time = 0.35 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.07 \[ \int \frac {e^{e^{e^x}} \left (30 x-15 x^2+e^x \left (-15-5 x+5 x^2\right )+e^{e^x} \left (e^{2 x} \left (15 x-5 x^2\right )+e^x \left (-15 x^2+5 x^3\right )\right )\right )}{9 x^4-6 x^5+x^6+e^{2 x} \left (9 x^2-6 x^3+x^4\right )+e^x \left (-18 x^3+12 x^4-2 x^5\right )} \, dx=-\frac {5\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}}}{x^2\,{\mathrm {e}}^x-3\,x\,{\mathrm {e}}^x+3\,x^2-x^3} \]
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