Integrand size = 36, antiderivative size = 16 \[ \int -\frac {40 e^{e^{\frac {5}{4 \log ^2\left (x^2\right )}}+\frac {5}{4 \log ^2\left (x^2\right )}}}{x \log ^3\left (x^2\right )} \, dx=8 e^{e^{\frac {5}{4 \log ^2\left (x^2\right )}}} \]
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Time = 0.09 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {12, 6847, 2320, 2225} \[ \int -\frac {40 e^{e^{\frac {5}{4 \log ^2\left (x^2\right )}}+\frac {5}{4 \log ^2\left (x^2\right )}}}{x \log ^3\left (x^2\right )} \, dx=8 e^{e^{\frac {5}{4 \log ^2\left (x^2\right )}}} \]
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Rule 12
Rule 2225
Rule 2320
Rule 6847
Rubi steps \begin{align*} \text {integral}& = -\left (40 \int \frac {e^{e^{\frac {5}{4 \log ^2\left (x^2\right )}}+\frac {5}{4 \log ^2\left (x^2\right )}}}{x \log ^3\left (x^2\right )} \, dx\right ) \\ & = -\left (20 \text {Subst}\left (\int \frac {e^{e^{\frac {5}{4 x^2}}+\frac {5}{4 x^2}}}{x^3} \, dx,x,\log \left (x^2\right )\right )\right ) \\ & = 10 \text {Subst}\left (\int e^{e^{5 x/4}+\frac {5 x}{4}} \, dx,x,\frac {1}{\log ^2\left (x^2\right )}\right ) \\ & = 8 \text {Subst}\left (\int e^x \, dx,x,e^{\frac {5}{4 \log ^2\left (x^2\right )}}\right ) \\ & = 8 e^{e^{\frac {5}{4 \log ^2\left (x^2\right )}}} \\ \end{align*}
Time = 0.14 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00 \[ \int -\frac {40 e^{e^{\frac {5}{4 \log ^2\left (x^2\right )}}+\frac {5}{4 \log ^2\left (x^2\right )}}}{x \log ^3\left (x^2\right )} \, dx=8 e^{e^{\frac {5}{4 \log ^2\left (x^2\right )}}} \]
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Time = 0.35 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.81
method | result | size |
risch | \(8 \,{\mathrm e}^{{\mathrm e}^{\frac {5}{4 \ln \left (x^{2}\right )^{2}}}}\) | \(13\) |
derivativedivides | \({\mathrm e}^{{\mathrm e}^{\frac {5}{4 \ln \left (x^{2}\right )^{2}}}+3 \ln \left (2\right )}\) | \(16\) |
default | \({\mathrm e}^{{\mathrm e}^{\frac {5}{4 \ln \left (x^{2}\right )^{2}}}+3 \ln \left (2\right )}\) | \(16\) |
parallelrisch | \({\mathrm e}^{{\mathrm e}^{\frac {5}{4 \ln \left (x^{2}\right )^{2}}}+3 \ln \left (2\right )}\) | \(16\) |
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Leaf count of result is larger than twice the leaf count of optimal. 47 vs. \(2 (15) = 30\).
Time = 0.26 (sec) , antiderivative size = 47, normalized size of antiderivative = 2.94 \[ \int -\frac {40 e^{e^{\frac {5}{4 \log ^2\left (x^2\right )}}+\frac {5}{4 \log ^2\left (x^2\right )}}}{x \log ^3\left (x^2\right )} \, dx=e^{\left (\frac {4 \, e^{\left (\frac {5}{4 \, \log \left (x^{2}\right )^{2}}\right )} \log \left (x^{2}\right )^{2} + 12 \, \log \left (2\right ) \log \left (x^{2}\right )^{2} + 5}{4 \, \log \left (x^{2}\right )^{2}} - \frac {5}{4 \, \log \left (x^{2}\right )^{2}}\right )} \]
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Time = 0.14 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int -\frac {40 e^{e^{\frac {5}{4 \log ^2\left (x^2\right )}}+\frac {5}{4 \log ^2\left (x^2\right )}}}{x \log ^3\left (x^2\right )} \, dx=8 e^{e^{\frac {5}{4 \log {\left (x^{2} \right )}^{2}}}} \]
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none
Time = 0.19 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.62 \[ \int -\frac {40 e^{e^{\frac {5}{4 \log ^2\left (x^2\right )}}+\frac {5}{4 \log ^2\left (x^2\right )}}}{x \log ^3\left (x^2\right )} \, dx=8 \, e^{\left (e^{\left (\frac {5}{16 \, \log \left (x\right )^{2}}\right )}\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 39 vs. \(2 (15) = 30\).
Time = 0.30 (sec) , antiderivative size = 39, normalized size of antiderivative = 2.44 \[ \int -\frac {40 e^{e^{\frac {5}{4 \log ^2\left (x^2\right )}}+\frac {5}{4 \log ^2\left (x^2\right )}}}{x \log ^3\left (x^2\right )} \, dx=8 \, e^{\left (\frac {4 \, e^{\left (\frac {5}{4 \, \log \left (x^{2}\right )^{2}}\right )} \log \left (x^{2}\right )^{2} + 5}{4 \, \log \left (x^{2}\right )^{2}} - \frac {5}{4 \, \log \left (x^{2}\right )^{2}}\right )} \]
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Time = 14.37 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.75 \[ \int -\frac {40 e^{e^{\frac {5}{4 \log ^2\left (x^2\right )}}+\frac {5}{4 \log ^2\left (x^2\right )}}}{x \log ^3\left (x^2\right )} \, dx=8\,{\mathrm {e}}^{{\mathrm {e}}^{\frac {5}{4\,{\ln \left (x^2\right )}^2}}} \]
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