Integrand size = 43, antiderivative size = 19 \[ \int e^{2+e^x+x+4 x^3+4 x^4 \log (x)} \left (1+e^x+12 x^2+4 x^3+16 x^3 \log (x)\right ) \, dx=e^{2+e^x+x+x^3 (4+4 x \log (x))} \]
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Time = 0.43 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.11, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.023, Rules used = {6838} \[ \int e^{2+e^x+x+4 x^3+4 x^4 \log (x)} \left (1+e^x+12 x^2+4 x^3+16 x^3 \log (x)\right ) \, dx=e^{4 x^3+x+e^x+2} x^{4 x^4} \]
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Rule 6838
Rubi steps \begin{align*} \text {integral}& = e^{2+e^x+x+4 x^3} x^{4 x^4} \\ \end{align*}
Time = 0.31 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.11 \[ \int e^{2+e^x+x+4 x^3+4 x^4 \log (x)} \left (1+e^x+12 x^2+4 x^3+16 x^3 \log (x)\right ) \, dx=e^{2+e^x+x+4 x^3} x^{4 x^4} \]
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Time = 0.18 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00
method | result | size |
derivativedivides | \({\mathrm e}^{4 x^{4} \ln \left (x \right )+{\mathrm e}^{x}+4 x^{3}+x +2}\) | \(19\) |
default | \({\mathrm e}^{4 x^{4} \ln \left (x \right )+{\mathrm e}^{x}+4 x^{3}+x +2}\) | \(19\) |
parallelrisch | \({\mathrm e}^{4 x^{4} \ln \left (x \right )+{\mathrm e}^{x}+4 x^{3}+x +2}\) | \(19\) |
risch | \(x^{4 x^{4}} {\mathrm e}^{2+{\mathrm e}^{x}+4 x^{3}+x}\) | \(20\) |
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none
Time = 0.26 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.95 \[ \int e^{2+e^x+x+4 x^3+4 x^4 \log (x)} \left (1+e^x+12 x^2+4 x^3+16 x^3 \log (x)\right ) \, dx=e^{\left (4 \, x^{4} \log \left (x\right ) + 4 \, x^{3} + x + e^{x} + 2\right )} \]
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Time = 0.13 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.05 \[ \int e^{2+e^x+x+4 x^3+4 x^4 \log (x)} \left (1+e^x+12 x^2+4 x^3+16 x^3 \log (x)\right ) \, dx=e^{4 x^{4} \log {\left (x \right )} + 4 x^{3} + x + e^{x} + 2} \]
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none
Time = 0.20 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.95 \[ \int e^{2+e^x+x+4 x^3+4 x^4 \log (x)} \left (1+e^x+12 x^2+4 x^3+16 x^3 \log (x)\right ) \, dx=e^{\left (4 \, x^{4} \log \left (x\right ) + 4 \, x^{3} + x + e^{x} + 2\right )} \]
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none
Time = 0.30 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.95 \[ \int e^{2+e^x+x+4 x^3+4 x^4 \log (x)} \left (1+e^x+12 x^2+4 x^3+16 x^3 \log (x)\right ) \, dx=e^{\left (4 \, x^{4} \log \left (x\right ) + 4 \, x^{3} + x + e^{x} + 2\right )} \]
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Time = 11.66 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.11 \[ \int e^{2+e^x+x+4 x^3+4 x^4 \log (x)} \left (1+e^x+12 x^2+4 x^3+16 x^3 \log (x)\right ) \, dx=x^{4\,x^4}\,{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^2\,{\mathrm {e}}^{4\,x^3}\,{\mathrm {e}}^x \]
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