Integrand size = 39, antiderivative size = 16 \[ \int \frac {216 e^x x^3+e^x \left (-864 x^3-216 x^4\right ) \log (x)+e^x \log ^2(x)}{\log ^2(x)} \, dx=e^x-\frac {216 e^x x^4}{\log (x)} \]
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\[ \int \frac {216 e^x x^3+e^x \left (-864 x^3-216 x^4\right ) \log (x)+e^x \log ^2(x)}{\log ^2(x)} \, dx=\int \frac {216 e^x x^3+e^x \left (-864 x^3-216 x^4\right ) \log (x)+e^x \log ^2(x)}{\log ^2(x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {e^x \left (216 x^3-216 x^3 (4+x) \log (x)+\log ^2(x)\right )}{\log ^2(x)} \, dx \\ & = \int \left (e^x+\frac {216 e^x x^3}{\log ^2(x)}-\frac {216 e^x x^3 (4+x)}{\log (x)}\right ) \, dx \\ & = 216 \int \frac {e^x x^3}{\log ^2(x)} \, dx-216 \int \frac {e^x x^3 (4+x)}{\log (x)} \, dx+\int e^x \, dx \\ & = e^x-216 \int \left (\frac {4 e^x x^3}{\log (x)}+\frac {e^x x^4}{\log (x)}\right ) \, dx+216 \int \frac {e^x x^3}{\log ^2(x)} \, dx \\ & = e^x+216 \int \frac {e^x x^3}{\log ^2(x)} \, dx-216 \int \frac {e^x x^4}{\log (x)} \, dx-864 \int \frac {e^x x^3}{\log (x)} \, dx \\ \end{align*}
Time = 0.08 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00 \[ \int \frac {216 e^x x^3+e^x \left (-864 x^3-216 x^4\right ) \log (x)+e^x \log ^2(x)}{\log ^2(x)} \, dx=e^x-\frac {216 e^x x^4}{\log (x)} \]
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Time = 0.06 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94
method | result | size |
risch | \({\mathrm e}^{x}-\frac {216 \,{\mathrm e}^{x} x^{4}}{\ln \left (x \right )}\) | \(15\) |
parallelrisch | \(-\frac {216 \,{\mathrm e}^{x} x^{4}-{\mathrm e}^{x} \ln \left (x \right )}{\ln \left (x \right )}\) | \(21\) |
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Time = 0.26 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.25 \[ \int \frac {216 e^x x^3+e^x \left (-864 x^3-216 x^4\right ) \log (x)+e^x \log ^2(x)}{\log ^2(x)} \, dx=-\frac {216 \, x^{4} e^{x} - e^{x} \log \left (x\right )}{\log \left (x\right )} \]
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Time = 0.07 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int \frac {216 e^x x^3+e^x \left (-864 x^3-216 x^4\right ) \log (x)+e^x \log ^2(x)}{\log ^2(x)} \, dx=\frac {\left (- 216 x^{4} + \log {\left (x \right )}\right ) e^{x}}{\log {\left (x \right )}} \]
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Time = 0.23 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int \frac {216 e^x x^3+e^x \left (-864 x^3-216 x^4\right ) \log (x)+e^x \log ^2(x)}{\log ^2(x)} \, dx=-\frac {216 \, x^{4} e^{x}}{\log \left (x\right )} + e^{x} \]
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Time = 0.26 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.25 \[ \int \frac {216 e^x x^3+e^x \left (-864 x^3-216 x^4\right ) \log (x)+e^x \log ^2(x)}{\log ^2(x)} \, dx=-\frac {216 \, x^{4} e^{x} - e^{x} \log \left (x\right )}{\log \left (x\right )} \]
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Time = 12.46 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int \frac {216 e^x x^3+e^x \left (-864 x^3-216 x^4\right ) \log (x)+e^x \log ^2(x)}{\log ^2(x)} \, dx={\mathrm {e}}^x-\frac {216\,x^4\,{\mathrm {e}}^x}{\ln \left (x\right )} \]
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