Integrand size = 95, antiderivative size = 25 \[ \int \frac {e^{x-16 e^{2+2 e^3} x^2-32 e^{2+2 e^3} x \log (3 x)-16 e^{2+2 e^3} \log ^2(3 x)} \left (x+e^{2+2 e^3} \left (-32 x-32 x^2\right )+e^{2+2 e^3} (-32-32 x) \log (3 x)\right )}{x} \, dx=16+e^{x-16 e^{2+2 e^3} (x+\log (3 x))^2} \]
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Leaf count is larger than twice the leaf count of optimal. \(64\) vs. \(2(25)=50\).
Time = 1.04 (sec) , antiderivative size = 64, normalized size of antiderivative = 2.56, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.011, Rules used = {6838} \[ \int \frac {e^{x-16 e^{2+2 e^3} x^2-32 e^{2+2 e^3} x \log (3 x)-16 e^{2+2 e^3} \log ^2(3 x)} \left (x+e^{2+2 e^3} \left (-32 x-32 x^2\right )+e^{2+2 e^3} (-32-32 x) \log (3 x)\right )}{x} \, dx=3^{-32 e^{2+2 e^3} x} x^{-32 e^{2+2 e^3} x} \exp \left (-16 e^{2+2 e^3} x^2+x-16 e^{2+2 e^3} \log ^2(3 x)\right ) \]
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Rule 6838
Rubi steps \begin{align*} \text {integral}& = 3^{-32 e^{2+2 e^3} x} \exp \left (x-16 e^{2+2 e^3} x^2-16 e^{2+2 e^3} \log ^2(3 x)\right ) x^{-32 e^{2+2 e^3} x} \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(51\) vs. \(2(25)=50\).
Time = 0.16 (sec) , antiderivative size = 51, normalized size of antiderivative = 2.04 \[ \int \frac {e^{x-16 e^{2+2 e^3} x^2-32 e^{2+2 e^3} x \log (3 x)-16 e^{2+2 e^3} \log ^2(3 x)} \left (x+e^{2+2 e^3} \left (-32 x-32 x^2\right )+e^{2+2 e^3} (-32-32 x) \log (3 x)\right )}{x} \, dx=e^{x-16 e^{2+2 e^3} x^2-32 e^{2+2 e^3} x \log (3 x)-16 e^{2+2 e^3} \log ^2(3 x)} \]
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Time = 0.26 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.80
method | result | size |
norman | \({\mathrm e}^{-16 \,{\mathrm e}^{2 \,{\mathrm e}^{3}+2} \ln \left (3 x \right )^{2}-32 \,{\mathrm e}^{2 \,{\mathrm e}^{3}+2} \ln \left (3 x \right ) x -16 \,{\mathrm e}^{2 \,{\mathrm e}^{3}+2} x^{2}+x}\) | \(45\) |
parallelrisch | \({\mathrm e}^{-16 \,{\mathrm e}^{2 \,{\mathrm e}^{3}+2} \ln \left (3 x \right )^{2}-32 \,{\mathrm e}^{2 \,{\mathrm e}^{3}+2} \ln \left (3 x \right ) x -16 \,{\mathrm e}^{2 \,{\mathrm e}^{3}+2} x^{2}+x}\) | \(45\) |
risch | \(\left (3 x \right )^{-32 \,{\mathrm e}^{2 \,{\mathrm e}^{3}+2} x} {\mathrm e}^{-16 \,{\mathrm e}^{2 \,{\mathrm e}^{3}+2} \ln \left (3 x \right )^{2}-16 \,{\mathrm e}^{2 \,{\mathrm e}^{3}+2} x^{2}+x}\) | \(46\) |
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Time = 0.29 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.76 \[ \int \frac {e^{x-16 e^{2+2 e^3} x^2-32 e^{2+2 e^3} x \log (3 x)-16 e^{2+2 e^3} \log ^2(3 x)} \left (x+e^{2+2 e^3} \left (-32 x-32 x^2\right )+e^{2+2 e^3} (-32-32 x) \log (3 x)\right )}{x} \, dx=e^{\left (-16 \, x^{2} e^{\left (2 \, e^{3} + 2\right )} - 32 \, x e^{\left (2 \, e^{3} + 2\right )} \log \left (3 \, x\right ) - 16 \, e^{\left (2 \, e^{3} + 2\right )} \log \left (3 \, x\right )^{2} + x\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 49 vs. \(2 (22) = 44\).
Time = 0.18 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.96 \[ \int \frac {e^{x-16 e^{2+2 e^3} x^2-32 e^{2+2 e^3} x \log (3 x)-16 e^{2+2 e^3} \log ^2(3 x)} \left (x+e^{2+2 e^3} \left (-32 x-32 x^2\right )+e^{2+2 e^3} (-32-32 x) \log (3 x)\right )}{x} \, dx=e^{- 16 x^{2} e^{2 + 2 e^{3}} - 32 x e^{2 + 2 e^{3}} \log {\left (3 x \right )} + x - 16 e^{2 + 2 e^{3}} \log {\left (3 x \right )}^{2}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 78 vs. \(2 (22) = 44\).
Time = 0.48 (sec) , antiderivative size = 78, normalized size of antiderivative = 3.12 \[ \int \frac {e^{x-16 e^{2+2 e^3} x^2-32 e^{2+2 e^3} x \log (3 x)-16 e^{2+2 e^3} \log ^2(3 x)} \left (x+e^{2+2 e^3} \left (-32 x-32 x^2\right )+e^{2+2 e^3} (-32-32 x) \log (3 x)\right )}{x} \, dx=e^{\left (-16 \, x^{2} e^{\left (2 \, e^{3} + 2\right )} - 32 \, x e^{\left (2 \, e^{3} + 2\right )} \log \left (3\right ) - 16 \, e^{\left (2 \, e^{3} + 2\right )} \log \left (3\right )^{2} - 32 \, x e^{\left (2 \, e^{3} + 2\right )} \log \left (x\right ) - 32 \, e^{\left (2 \, e^{3} + 2\right )} \log \left (3\right ) \log \left (x\right ) - 16 \, e^{\left (2 \, e^{3} + 2\right )} \log \left (x\right )^{2} + x\right )} \]
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Time = 0.40 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.76 \[ \int \frac {e^{x-16 e^{2+2 e^3} x^2-32 e^{2+2 e^3} x \log (3 x)-16 e^{2+2 e^3} \log ^2(3 x)} \left (x+e^{2+2 e^3} \left (-32 x-32 x^2\right )+e^{2+2 e^3} (-32-32 x) \log (3 x)\right )}{x} \, dx=e^{\left (-16 \, x^{2} e^{\left (2 \, e^{3} + 2\right )} - 32 \, x e^{\left (2 \, e^{3} + 2\right )} \log \left (3 \, x\right ) - 16 \, e^{\left (2 \, e^{3} + 2\right )} \log \left (3 \, x\right )^{2} + x\right )} \]
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Time = 12.28 (sec) , antiderivative size = 87, normalized size of antiderivative = 3.48 \[ \int \frac {e^{x-16 e^{2+2 e^3} x^2-32 e^{2+2 e^3} x \log (3 x)-16 e^{2+2 e^3} \log ^2(3 x)} \left (x+e^{2+2 e^3} \left (-32 x-32 x^2\right )+e^{2+2 e^3} (-32-32 x) \log (3 x)\right )}{x} \, dx=\frac {{\mathrm {e}}^{-16\,{\mathrm {e}}^{2\,{\mathrm {e}}^3}\,{\mathrm {e}}^2\,{\ln \left (3\right )}^2}\,{\mathrm {e}}^{-16\,x^2\,{\mathrm {e}}^{2\,{\mathrm {e}}^3}\,{\mathrm {e}}^2}\,{\mathrm {e}}^{-16\,{\mathrm {e}}^{2\,{\mathrm {e}}^3}\,{\mathrm {e}}^2\,{\ln \left (x\right )}^2}\,{\mathrm {e}}^x}{3^{32\,x\,{\mathrm {e}}^{2\,{\mathrm {e}}^3}\,{\mathrm {e}}^2}\,x^{32\,{\mathrm {e}}^{2\,{\mathrm {e}}^3}\,{\mathrm {e}}^2\,\ln \left (3\right )}\,x^{32\,x\,{\mathrm {e}}^{2\,{\mathrm {e}}^3}\,{\mathrm {e}}^2}} \]
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