Integrand size = 34, antiderivative size = 22 \[ \int \frac {2 x^2+e^{3968-1512 x+144 x^2} x \left (1-1512 x+288 x^2\right )}{x} \, dx=e^{-1+9 (-9+3 (-4+x)+x)^2} x+x^2 \]
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Time = 0.03 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.50, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {14, 2326} \[ \int \frac {2 x^2+e^{3968-1512 x+144 x^2} x \left (1-1512 x+288 x^2\right )}{x} \, dx=x^2+\frac {e^{144 x^2-1512 x+3968} \left (21 x-4 x^2\right )}{21-4 x} \]
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Rule 14
Rule 2326
Rubi steps \begin{align*} \text {integral}& = \int \left (2 x+e^{3968-1512 x+144 x^2} \left (1-1512 x+288 x^2\right )\right ) \, dx \\ & = x^2+\int e^{3968-1512 x+144 x^2} \left (1-1512 x+288 x^2\right ) \, dx \\ & = x^2+\frac {e^{3968-1512 x+144 x^2} \left (21 x-4 x^2\right )}{21-4 x} \\ \end{align*}
Time = 0.25 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.82 \[ \int \frac {2 x^2+e^{3968-1512 x+144 x^2} x \left (1-1512 x+288 x^2\right )}{x} \, dx=x \left (e^{8 \left (496-189 x+18 x^2\right )}+x\right ) \]
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Time = 0.16 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.82
method | result | size |
default | \({\mathrm e}^{\ln \left (x \right )+144 x^{2}-1512 x +3968}+x^{2}\) | \(18\) |
norman | \({\mathrm e}^{\ln \left (x \right )+144 x^{2}-1512 x +3968}+x^{2}\) | \(18\) |
parallelrisch | \({\mathrm e}^{\ln \left (x \right )+144 x^{2}-1512 x +3968}+x^{2}\) | \(18\) |
parts | \({\mathrm e}^{\ln \left (x \right )+144 x^{2}-1512 x +3968}+x^{2}\) | \(18\) |
risch | \(x \,{\mathrm e}^{8 \left (6 x -31\right ) \left (3 x -16\right )}+x^{2}\) | \(20\) |
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Time = 0.27 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.77 \[ \int \frac {2 x^2+e^{3968-1512 x+144 x^2} x \left (1-1512 x+288 x^2\right )}{x} \, dx=x^{2} + e^{\left (144 \, x^{2} - 1512 \, x + \log \left (x\right ) + 3968\right )} \]
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Time = 0.06 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.68 \[ \int \frac {2 x^2+e^{3968-1512 x+144 x^2} x \left (1-1512 x+288 x^2\right )}{x} \, dx=x^{2} + x e^{144 x^{2} - 1512 x + 3968} \]
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Result contains higher order function than in optimal. Order 4 vs. order 3.
Time = 0.34 (sec) , antiderivative size = 153, normalized size of antiderivative = 6.95 \[ \int \frac {2 x^2+e^{3968-1512 x+144 x^2} x \left (1-1512 x+288 x^2\right )}{x} \, dx=-\frac {1}{24} i \, \sqrt {\pi } \operatorname {erf}\left (12 i \, x - 63 i\right ) e^{\left (-1\right )} + x^{2} - \frac {1}{12} \, {\left (\frac {{\left (4 \, x - 21\right )}^{3} \Gamma \left (\frac {3}{2}, -9 \, {\left (4 \, x - 21\right )}^{2}\right )}{\left (-{\left (4 \, x - 21\right )}^{2}\right )^{\frac {3}{2}}} - \frac {3969 \, \sqrt {\pi } {\left (4 \, x - 21\right )} {\left (\operatorname {erf}\left (3 \, \sqrt {-{\left (4 \, x - 21\right )}^{2}}\right ) - 1\right )}}{\sqrt {-{\left (4 \, x - 21\right )}^{2}}} - 126 \, e^{\left (9 \, {\left (4 \, x - 21\right )}^{2}\right )}\right )} e^{\left (-1\right )} - \frac {21}{4} \, {\left (\frac {63 \, \sqrt {\pi } {\left (4 \, x - 21\right )} {\left (\operatorname {erf}\left (3 \, \sqrt {-{\left (4 \, x - 21\right )}^{2}}\right ) - 1\right )}}{\sqrt {-{\left (4 \, x - 21\right )}^{2}}} + e^{\left (9 \, {\left (4 \, x - 21\right )}^{2}\right )}\right )} e^{\left (-1\right )} \]
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Time = 0.28 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.77 \[ \int \frac {2 x^2+e^{3968-1512 x+144 x^2} x \left (1-1512 x+288 x^2\right )}{x} \, dx=x^{2} + x e^{\left (144 \, x^{2} - 1512 \, x + 3968\right )} \]
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Time = 13.98 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.82 \[ \int \frac {2 x^2+e^{3968-1512 x+144 x^2} x \left (1-1512 x+288 x^2\right )}{x} \, dx=x^2+x\,{\mathrm {e}}^{-1512\,x}\,{\mathrm {e}}^{3968}\,{\mathrm {e}}^{144\,x^2} \]
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