Integrand size = 36, antiderivative size = 16 \[ \int e^{4096 e^{8 x^2} x^2} \left (1+e^{8 x^2} \left (8192 x^2+65536 x^4\right )\right ) \, dx=e^{4096 e^{8 x^2} x^2} x \]
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Leaf count is larger than twice the leaf count of optimal. \(54\) vs. \(2(16)=32\).
Time = 0.02 (sec) , antiderivative size = 54, normalized size of antiderivative = 3.38, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.028, Rules used = {2326} \[ \int e^{4096 e^{8 x^2} x^2} \left (1+e^{8 x^2} \left (8192 x^2+65536 x^4\right )\right ) \, dx=\frac {e^{4096 e^{8 x^2} x^2+8 x^2} \left (8 x^4+x^2\right )}{e^{8 x^2} x+8 e^{8 x^2} x^3} \]
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Rule 2326
Rubi steps \begin{align*} \text {integral}& = \frac {e^{8 x^2+4096 e^{8 x^2} x^2} \left (x^2+8 x^4\right )}{e^{8 x^2} x+8 e^{8 x^2} x^3} \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00 \[ \int e^{4096 e^{8 x^2} x^2} \left (1+e^{8 x^2} \left (8192 x^2+65536 x^4\right )\right ) \, dx=e^{4096 e^{8 x^2} x^2} x \]
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Time = 0.71 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94
method | result | size |
risch | \({\mathrm e}^{4096 x^{2} {\mathrm e}^{8 x^{2}}} x\) | \(15\) |
norman | \({\mathrm e}^{4096 x^{2} {\mathrm e}^{8 x^{2}}} x\) | \(17\) |
parallelrisch | \({\mathrm e}^{4096 x^{2} {\mathrm e}^{8 x^{2}}} x\) | \(17\) |
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Time = 0.25 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int e^{4096 e^{8 x^2} x^2} \left (1+e^{8 x^2} \left (8192 x^2+65536 x^4\right )\right ) \, dx=x e^{\left (4096 \, x^{2} e^{\left (8 \, x^{2}\right )}\right )} \]
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Time = 1.45 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int e^{4096 e^{8 x^2} x^2} \left (1+e^{8 x^2} \left (8192 x^2+65536 x^4\right )\right ) \, dx=x e^{4096 x^{2} e^{8 x^{2}}} \]
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Time = 0.21 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int e^{4096 e^{8 x^2} x^2} \left (1+e^{8 x^2} \left (8192 x^2+65536 x^4\right )\right ) \, dx=x e^{\left (4096 \, x^{2} e^{\left (8 \, x^{2}\right )}\right )} \]
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\[ \int e^{4096 e^{8 x^2} x^2} \left (1+e^{8 x^2} \left (8192 x^2+65536 x^4\right )\right ) \, dx=\int { {\left (8192 \, {\left (8 \, x^{4} + x^{2}\right )} e^{\left (8 \, x^{2}\right )} + 1\right )} e^{\left (4096 \, x^{2} e^{\left (8 \, x^{2}\right )}\right )} \,d x } \]
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Time = 0.14 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int e^{4096 e^{8 x^2} x^2} \left (1+e^{8 x^2} \left (8192 x^2+65536 x^4\right )\right ) \, dx=x\,{\mathrm {e}}^{4096\,x^2\,{\mathrm {e}}^{8\,x^2}} \]
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