Integrand size = 34, antiderivative size = 23 \[ \int \frac {e^{e^x} \left (96+32 x+e^x \left (96 x+16 x^2\right )\right )}{i \pi +\log (25)} \, dx=-3+\frac {16 e^{e^x} x (6+x)}{i \pi +\log (25)} \]
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Time = 0.02 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.04, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {12, 2326} \[ \int \frac {e^{e^x} \left (96+32 x+e^x \left (96 x+16 x^2\right )\right )}{i \pi +\log (25)} \, dx=\frac {16 e^{e^x} \left (x^2+6 x\right )}{\log (25)+i \pi } \]
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Rule 12
Rule 2326
Rubi steps \begin{align*} \text {integral}& = \frac {\int e^{e^x} \left (96+32 x+e^x \left (96 x+16 x^2\right )\right ) \, dx}{i \pi +\log (25)} \\ & = \frac {16 e^{e^x} \left (6 x+x^2\right )}{i \pi +\log (25)} \\ \end{align*}
Time = 0.09 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.91 \[ \int \frac {e^{e^x} \left (96+32 x+e^x \left (96 x+16 x^2\right )\right )}{i \pi +\log (25)} \, dx=\frac {16 e^{e^x} x (6+x)}{i \pi +\log (25)} \]
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Time = 0.09 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.09
method | result | size |
risch | \(\frac {\left (16 x^{2}+96 x \right ) {\mathrm e}^{{\mathrm e}^{x}}}{2 \ln \left (5\right )+i \pi }\) | \(25\) |
parallelrisch | \(\frac {16 \,{\mathrm e}^{{\mathrm e}^{x}} x^{2}+96 x \,{\mathrm e}^{{\mathrm e}^{x}}}{2 \ln \left (5\right )+i \pi }\) | \(28\) |
norman | \(-\frac {96 \left (i \pi -2 \ln \left (5\right )\right ) x \,{\mathrm e}^{{\mathrm e}^{x}}}{\pi ^{2}+4 \ln \left (5\right )^{2}}-\frac {16 \left (i \pi -2 \ln \left (5\right )\right ) x^{2} {\mathrm e}^{{\mathrm e}^{x}}}{\pi ^{2}+4 \ln \left (5\right )^{2}}\) | \(58\) |
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Time = 0.25 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.96 \[ \int \frac {e^{e^x} \left (96+32 x+e^x \left (96 x+16 x^2\right )\right )}{i \pi +\log (25)} \, dx=\frac {16 \, {\left (x^{2} + 6 \, x\right )} e^{\left (e^{x}\right )}}{i \, \pi + 2 \, \log \left (5\right )} \]
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Time = 0.22 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.87 \[ \int \frac {e^{e^x} \left (96+32 x+e^x \left (96 x+16 x^2\right )\right )}{i \pi +\log (25)} \, dx=\frac {\left (16 x^{2} + 96 x\right ) e^{e^{x}}}{2 \log {\left (5 \right )} + i \pi } \]
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\[ \int \frac {e^{e^x} \left (96+32 x+e^x \left (96 x+16 x^2\right )\right )}{i \pi +\log (25)} \, dx=\int { \frac {16 \, {\left ({\left (x^{2} + 6 \, x\right )} e^{x} + 2 \, x + 6\right )} e^{\left (e^{x}\right )}}{i \, \pi + 2 \, \log \left (5\right )} \,d x } \]
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Time = 0.27 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.48 \[ \int \frac {e^{e^x} \left (96+32 x+e^x \left (96 x+16 x^2\right )\right )}{i \pi +\log (25)} \, dx=\frac {16 \, {\left (x^{2} e^{\left (x + e^{x}\right )} + 6 \, x e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}}{i \, \pi + 2 \, \log \left (5\right )} \]
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Time = 0.31 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.30 \[ \int \frac {e^{e^x} \left (96+32 x+e^x \left (96 x+16 x^2\right )\right )}{i \pi +\log (25)} \, dx=-\frac {16\,x\,{\mathrm {e}}^{{\mathrm {e}}^x}\,\left (x+6\right )\,\left (-\ln \left (25\right )+\Pi \,1{}\mathrm {i}\right )}{\Pi ^2+4\,{\ln \left (5\right )}^2} \]
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