Integrand size = 48, antiderivative size = 24 \[ \int \frac {e^{\frac {16+6 x-x^2+24 x^3+9 x^6}{x}} \left (-16+x-x^2+48 x^3+45 x^6\right )}{x} \, dx=2+e^{6-x+\frac {\left (4+3 x^3\right )^2}{x}} x \]
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Leaf count is larger than twice the leaf count of optimal. \(94\) vs. \(2(24)=48\).
Time = 0.09 (sec) , antiderivative size = 94, normalized size of antiderivative = 3.92, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.021, Rules used = {2326} \[ \int \frac {e^{\frac {16+6 x-x^2+24 x^3+9 x^6}{x}} \left (-16+x-x^2+48 x^3+45 x^6\right )}{x} \, dx=-\frac {e^{\frac {9 x^6+24 x^3-x^2+6 x+16}{x}} \left (-45 x^6-48 x^3+x^2+16\right )}{x \left (\frac {2 \left (27 x^5+36 x^2-x+3\right )}{x}-\frac {9 x^6+24 x^3-x^2+6 x+16}{x^2}\right )} \]
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Rule 2326
Rubi steps \begin{align*} \text {integral}& = -\frac {e^{\frac {16+6 x-x^2+24 x^3+9 x^6}{x}} \left (16+x^2-48 x^3-45 x^6\right )}{x \left (\frac {2 \left (3-x+36 x^2+27 x^5\right )}{x}-\frac {16+6 x-x^2+24 x^3+9 x^6}{x^2}\right )} \\ \end{align*}
Time = 0.05 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00 \[ \int \frac {e^{\frac {16+6 x-x^2+24 x^3+9 x^6}{x}} \left (-16+x-x^2+48 x^3+45 x^6\right )}{x} \, dx=e^{6+\frac {16}{x}-x+24 x^2+9 x^5} x \]
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Time = 0.86 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.17
method | result | size |
gosper | \(x \,{\mathrm e}^{\frac {9 x^{6}+24 x^{3}-x^{2}+6 x +16}{x}}\) | \(28\) |
norman | \(x \,{\mathrm e}^{\frac {9 x^{6}+24 x^{3}-x^{2}+6 x +16}{x}}\) | \(28\) |
risch | \(x \,{\mathrm e}^{\frac {9 x^{6}+24 x^{3}-x^{2}+6 x +16}{x}}\) | \(28\) |
parallelrisch | \(x \,{\mathrm e}^{\frac {9 x^{6}+24 x^{3}-x^{2}+6 x +16}{x}}\) | \(28\) |
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none
Time = 0.24 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.12 \[ \int \frac {e^{\frac {16+6 x-x^2+24 x^3+9 x^6}{x}} \left (-16+x-x^2+48 x^3+45 x^6\right )}{x} \, dx=x e^{\left (\frac {9 \, x^{6} + 24 \, x^{3} - x^{2} + 6 \, x + 16}{x}\right )} \]
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Time = 0.07 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.92 \[ \int \frac {e^{\frac {16+6 x-x^2+24 x^3+9 x^6}{x}} \left (-16+x-x^2+48 x^3+45 x^6\right )}{x} \, dx=x e^{\frac {9 x^{6} + 24 x^{3} - x^{2} + 6 x + 16}{x}} \]
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none
Time = 0.25 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.96 \[ \int \frac {e^{\frac {16+6 x-x^2+24 x^3+9 x^6}{x}} \left (-16+x-x^2+48 x^3+45 x^6\right )}{x} \, dx=x e^{\left (9 \, x^{5} + 24 \, x^{2} - x + \frac {16}{x} + 6\right )} \]
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Time = 0.26 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.12 \[ \int \frac {e^{\frac {16+6 x-x^2+24 x^3+9 x^6}{x}} \left (-16+x-x^2+48 x^3+45 x^6\right )}{x} \, dx=x e^{\left (\frac {9 \, x^{6} + 24 \, x^{3} - x^{2} + 6 \, x + 16}{x}\right )} \]
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Time = 9.59 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {e^{\frac {16+6 x-x^2+24 x^3+9 x^6}{x}} \left (-16+x-x^2+48 x^3+45 x^6\right )}{x} \, dx=x\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^6\,{\mathrm {e}}^{9\,x^5}\,{\mathrm {e}}^{16/x}\,{\mathrm {e}}^{24\,x^2} \]
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