Integrand size = 89, antiderivative size = 28 \[ \int \frac {e^{-3+\frac {e^{-3+e^{512+2 e^2+64 x+2 x^2}}}{x}} \left (4 e^3 x+e^{e^{512+2 e^2+64 x+2 x^2}} \left (-4+e^{512+2 e^2+64 x+2 x^2} \left (256 x+16 x^2\right )\right )\right )}{x} \, dx=4 e^{\frac {e^{-3+e^{2 e^2+2 (16+x)^2}}}{x}} x \]
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Leaf count is larger than twice the leaf count of optimal. \(154\) vs. \(2(28)=56\).
Time = 0.22 (sec) , antiderivative size = 154, normalized size of antiderivative = 5.50, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.011, Rules used = {2326} \[ \int \frac {e^{-3+\frac {e^{-3+e^{512+2 e^2+64 x+2 x^2}}}{x}} \left (4 e^3 x+e^{e^{512+2 e^2+64 x+2 x^2}} \left (-4+e^{512+2 e^2+64 x+2 x^2} \left (256 x+16 x^2\right )\right )\right )}{x} \, dx=\frac {4 \left (1-4 e^{2 x^2+64 x+2 \left (256+e^2\right )} \left (x^2+16 x\right )\right ) \exp \left (e^{2 x^2+64 x+2 \left (256+e^2\right )}+\frac {e^{e^{2 x^2+64 x+2 \left (256+e^2\right )}-3}}{x}-3\right )}{x \left (\frac {e^{e^{2 x^2+64 x+2 \left (256+e^2\right )}-3}}{x^2}-\frac {4 (x+16) \exp \left (2 x^2+e^{2 x^2+64 x+2 \left (256+e^2\right )}+64 x+2 e^2+509\right )}{x}\right )} \]
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Rule 2326
Rubi steps \begin{align*} \text {integral}& = \frac {4 \exp \left (-3+e^{2 \left (256+e^2\right )+64 x+2 x^2}+\frac {e^{-3+e^{2 \left (256+e^2\right )+64 x+2 x^2}}}{x}\right ) \left (1-4 e^{2 \left (256+e^2\right )+64 x+2 x^2} \left (16 x+x^2\right )\right )}{x \left (\frac {e^{-3+e^{2 \left (256+e^2\right )+64 x+2 x^2}}}{x^2}-\frac {4 \exp \left (509+2 e^2+e^{2 \left (256+e^2\right )+64 x+2 x^2}+64 x+2 x^2\right ) (16+x)}{x}\right )} \\ \end{align*}
Time = 0.25 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.93 \[ \int \frac {e^{-3+\frac {e^{-3+e^{512+2 e^2+64 x+2 x^2}}}{x}} \left (4 e^3 x+e^{e^{512+2 e^2+64 x+2 x^2}} \left (-4+e^{512+2 e^2+64 x+2 x^2} \left (256 x+16 x^2\right )\right )\right )}{x} \, dx=4 e^{\frac {e^{-3+e^{2 \left (e^2+(16+x)^2\right )}}}{x}} x \]
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Time = 8.31 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.96
method | result | size |
risch | \(4 x \,{\mathrm e}^{\frac {{\mathrm e}^{{\mathrm e}^{2 \,{\mathrm e}^{2}+2 x^{2}+64 x +512}-3}}{x}}\) | \(27\) |
parallelrisch | \(4 x \,{\mathrm e}^{\frac {{\mathrm e}^{{\mathrm e}^{2 \,{\mathrm e}^{2}+2 x^{2}+64 x +512}} {\mathrm e}^{-3}}{x}}\) | \(27\) |
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Time = 0.25 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.32 \[ \int \frac {e^{-3+\frac {e^{-3+e^{512+2 e^2+64 x+2 x^2}}}{x}} \left (4 e^3 x+e^{e^{512+2 e^2+64 x+2 x^2}} \left (-4+e^{512+2 e^2+64 x+2 x^2} \left (256 x+16 x^2\right )\right )\right )}{x} \, dx=4 \, x e^{\left (-\frac {{\left (3 \, x e^{3} - e^{\left (e^{\left (2 \, x^{2} + 64 \, x + 2 \, e^{2} + 512\right )}\right )}\right )} e^{\left (-3\right )}}{x} + 3\right )} \]
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Time = 54.40 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.96 \[ \int \frac {e^{-3+\frac {e^{-3+e^{512+2 e^2+64 x+2 x^2}}}{x}} \left (4 e^3 x+e^{e^{512+2 e^2+64 x+2 x^2}} \left (-4+e^{512+2 e^2+64 x+2 x^2} \left (256 x+16 x^2\right )\right )\right )}{x} \, dx=4 x e^{\frac {e^{e^{2 x^{2} + 64 x + 2 e^{2} + 512}}}{x e^{3}}} \]
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Time = 0.27 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.93 \[ \int \frac {e^{-3+\frac {e^{-3+e^{512+2 e^2+64 x+2 x^2}}}{x}} \left (4 e^3 x+e^{e^{512+2 e^2+64 x+2 x^2}} \left (-4+e^{512+2 e^2+64 x+2 x^2} \left (256 x+16 x^2\right )\right )\right )}{x} \, dx=4 \, x e^{\left (\frac {e^{\left (e^{\left (2 \, x^{2} + 64 \, x + 2 \, e^{2} + 512\right )} - 3\right )}}{x}\right )} \]
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\[ \int \frac {e^{-3+\frac {e^{-3+e^{512+2 e^2+64 x+2 x^2}}}{x}} \left (4 e^3 x+e^{e^{512+2 e^2+64 x+2 x^2}} \left (-4+e^{512+2 e^2+64 x+2 x^2} \left (256 x+16 x^2\right )\right )\right )}{x} \, dx=\int { \frac {4 \, {\left (x e^{3} + {\left (4 \, {\left (x^{2} + 16 \, x\right )} e^{\left (2 \, x^{2} + 64 \, x + 2 \, e^{2} + 512\right )} - 1\right )} e^{\left (e^{\left (2 \, x^{2} + 64 \, x + 2 \, e^{2} + 512\right )}\right )}\right )} e^{\left (\frac {e^{\left (e^{\left (2 \, x^{2} + 64 \, x + 2 \, e^{2} + 512\right )} - 3\right )}}{x} - 3\right )}}{x} \,d x } \]
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Time = 11.19 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.04 \[ \int \frac {e^{-3+\frac {e^{-3+e^{512+2 e^2+64 x+2 x^2}}}{x}} \left (4 e^3 x+e^{e^{512+2 e^2+64 x+2 x^2}} \left (-4+e^{512+2 e^2+64 x+2 x^2} \left (256 x+16 x^2\right )\right )\right )}{x} \, dx=4\,x\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{{\mathrm {e}}^{2\,{\mathrm {e}}^2}\,{\mathrm {e}}^{64\,x}\,{\mathrm {e}}^{512}\,{\mathrm {e}}^{2\,x^2}}\,{\mathrm {e}}^{-3}}{x}} \]
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