Integrand size = 60, antiderivative size = 24 \[ \int \frac {e^{2 e^3 x+x \log (x)+e^{2 e^{2 e^5}} \left (2 e^3+\log (x)\right )} \left (e^{2 e^{2 e^5}}+x+2 e^3 x+x \log (x)\right )}{x} \, dx=e^{\left (e^{2 e^{2 e^5}}+x\right ) \left (2 e^3+\log (x)\right )} \]
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Time = 0.78 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.38, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.033, Rules used = {6, 6838} \[ \int \frac {e^{2 e^3 x+x \log (x)+e^{2 e^{2 e^5}} \left (2 e^3+\log (x)\right )} \left (e^{2 e^{2 e^5}}+x+2 e^3 x+x \log (x)\right )}{x} \, dx=x^x e^{2 e^3 x+e^{2 e^{2 e^5}} \left (\log (x)+2 e^3\right )} \]
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Rule 6
Rule 6838
Rubi steps \begin{align*} \text {integral}& = \int \frac {\exp \left (2 e^3 x+x \log (x)+e^{2 e^{2 e^5}} \left (2 e^3+\log (x)\right )\right ) \left (e^{2 e^{2 e^5}}+\left (1+2 e^3\right ) x+x \log (x)\right )}{x} \, dx \\ & = e^{2 e^3 x+e^{2 e^{2 e^5}} \left (2 e^3+\log (x)\right )} x^x \\ \end{align*}
Time = 0.24 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.38 \[ \int \frac {e^{2 e^3 x+x \log (x)+e^{2 e^{2 e^5}} \left (2 e^3+\log (x)\right )} \left (e^{2 e^{2 e^5}}+x+2 e^3 x+x \log (x)\right )}{x} \, dx=e^{2 e^3 x+e^{2 e^{2 e^5}} \left (2 e^3+\log (x)\right )} x^x \]
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Time = 0.20 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.17
method | result | size |
norman | \({\mathrm e}^{\left (\ln \left (x \right )+2 \,{\mathrm e}^{3}\right ) {\mathrm e}^{2 \,{\mathrm e}^{2 \,{\mathrm e}^{5}}}+x \ln \left (x \right )+2 x \,{\mathrm e}^{3}}\) | \(28\) |
parallelrisch | \({\mathrm e}^{\left (\ln \left (x \right )+2 \,{\mathrm e}^{3}\right ) {\mathrm e}^{2 \,{\mathrm e}^{2 \,{\mathrm e}^{5}}}+x \ln \left (x \right )+2 x \,{\mathrm e}^{3}}\) | \(28\) |
risch | \(x^{x} x^{{\mathrm e}^{2 \,{\mathrm e}^{2 \,{\mathrm e}^{5}}}} {\mathrm e}^{2 \,{\mathrm e}^{2 \,{\mathrm e}^{2 \,{\mathrm e}^{5}}+3}+2 x \,{\mathrm e}^{3}}\) | \(34\) |
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Time = 0.31 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.12 \[ \int \frac {e^{2 e^3 x+x \log (x)+e^{2 e^{2 e^5}} \left (2 e^3+\log (x)\right )} \left (e^{2 e^{2 e^5}}+x+2 e^3 x+x \log (x)\right )}{x} \, dx=e^{\left (2 \, x e^{3} + {\left (2 \, e^{3} + \log \left (x\right )\right )} e^{\left (2 \, e^{\left (2 \, e^{5}\right )}\right )} + x \log \left (x\right )\right )} \]
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Time = 0.12 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.29 \[ \int \frac {e^{2 e^3 x+x \log (x)+e^{2 e^{2 e^5}} \left (2 e^3+\log (x)\right )} \left (e^{2 e^{2 e^5}}+x+2 e^3 x+x \log (x)\right )}{x} \, dx=e^{x \log {\left (x \right )} + 2 x e^{3} + \left (\log {\left (x \right )} + 2 e^{3}\right ) e^{2 e^{2 e^{5}}}} \]
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Time = 0.34 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.42 \[ \int \frac {e^{2 e^3 x+x \log (x)+e^{2 e^{2 e^5}} \left (2 e^3+\log (x)\right )} \left (e^{2 e^{2 e^5}}+x+2 e^3 x+x \log (x)\right )}{x} \, dx=e^{\left (2 \, x e^{3} + x \log \left (x\right ) + e^{\left (2 \, e^{\left (2 \, e^{5}\right )}\right )} \log \left (x\right ) + 2 \, e^{\left (2 \, e^{\left (2 \, e^{5}\right )} + 3\right )}\right )} \]
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Time = 0.30 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.42 \[ \int \frac {e^{2 e^3 x+x \log (x)+e^{2 e^{2 e^5}} \left (2 e^3+\log (x)\right )} \left (e^{2 e^{2 e^5}}+x+2 e^3 x+x \log (x)\right )}{x} \, dx=e^{\left (2 \, x e^{3} + x \log \left (x\right ) + e^{\left (2 \, e^{\left (2 \, e^{5}\right )}\right )} \log \left (x\right ) + 2 \, e^{\left (2 \, e^{\left (2 \, e^{5}\right )} + 3\right )}\right )} \]
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Time = 14.98 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.33 \[ \int \frac {e^{2 e^3 x+x \log (x)+e^{2 e^{2 e^5}} \left (2 e^3+\log (x)\right )} \left (e^{2 e^{2 e^5}}+x+2 e^3 x+x \log (x)\right )}{x} \, dx=x^{x+{\mathrm {e}}^{2\,{\mathrm {e}}^{2\,{\mathrm {e}}^5}}}\,{\mathrm {e}}^{2\,{\mathrm {e}}^3\,{\mathrm {e}}^{2\,{\mathrm {e}}^{2\,{\mathrm {e}}^5}}}\,{\mathrm {e}}^{2\,x\,{\mathrm {e}}^3} \]
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