Integrand size = 51, antiderivative size = 26 \[ \int \frac {-25 \log (5)+e^{\frac {e^x x+2 x^3 \log (5)}{\log (5)}} \left (e^x (-1-x)-6 x^2 \log (5)\right )}{25 \log (5)} \, dx=2-\frac {1}{25} e^{2 x^3+\frac {e^x x}{\log (5)}}-x \]
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Time = 0.07 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.96, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.039, Rules used = {12, 6838} \[ \int \frac {-25 \log (5)+e^{\frac {e^x x+2 x^3 \log (5)}{\log (5)}} \left (e^x (-1-x)-6 x^2 \log (5)\right )}{25 \log (5)} \, dx=-\frac {1}{25} e^{2 x^3+\frac {e^x x}{\log (5)}}-x \]
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Rule 12
Rule 6838
Rubi steps \begin{align*} \text {integral}& = \frac {\int \left (-25 \log (5)+e^{\frac {e^x x+2 x^3 \log (5)}{\log (5)}} \left (e^x (-1-x)-6 x^2 \log (5)\right )\right ) \, dx}{25 \log (5)} \\ & = -x+\frac {\int e^{\frac {e^x x+2 x^3 \log (5)}{\log (5)}} \left (e^x (-1-x)-6 x^2 \log (5)\right ) \, dx}{25 \log (5)} \\ & = -\frac {1}{25} e^{2 x^3+\frac {e^x x}{\log (5)}}-x \\ \end{align*}
Time = 0.75 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.96 \[ \int \frac {-25 \log (5)+e^{\frac {e^x x+2 x^3 \log (5)}{\log (5)}} \left (e^x (-1-x)-6 x^2 \log (5)\right )}{25 \log (5)} \, dx=-\frac {1}{25} e^{2 x^3+\frac {e^x x}{\log (5)}}-x \]
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Time = 0.18 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.92
method | result | size |
risch | \(-x -\frac {{\mathrm e}^{\frac {x \left (2 x^{2} \ln \left (5\right )+{\mathrm e}^{x}\right )}{\ln \left (5\right )}}}{25}\) | \(24\) |
norman | \(-x -\frac {{\mathrm e}^{\frac {{\mathrm e}^{x} x +2 x^{3} \ln \left (5\right )}{\ln \left (5\right )}}}{25}\) | \(25\) |
parallelrisch | \(\frac {-\ln \left (5\right ) {\mathrm e}^{\frac {x \left (2 x^{2} \ln \left (5\right )+{\mathrm e}^{x}\right )}{\ln \left (5\right )}}-25 x \ln \left (5\right )}{25 \ln \left (5\right )}\) | \(34\) |
default | \(\frac {-\ln \left (5\right ) {\mathrm e}^{\frac {{\mathrm e}^{x} x +2 x^{3} \ln \left (5\right )}{\ln \left (5\right )}}-25 x \ln \left (5\right )}{25 \ln \left (5\right )}\) | \(35\) |
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Time = 0.27 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.92 \[ \int \frac {-25 \log (5)+e^{\frac {e^x x+2 x^3 \log (5)}{\log (5)}} \left (e^x (-1-x)-6 x^2 \log (5)\right )}{25 \log (5)} \, dx=-x - \frac {1}{25} \, e^{\left (\frac {2 \, x^{3} \log \left (5\right ) + x e^{x}}{\log \left (5\right )}\right )} \]
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Time = 0.12 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.85 \[ \int \frac {-25 \log (5)+e^{\frac {e^x x+2 x^3 \log (5)}{\log (5)}} \left (e^x (-1-x)-6 x^2 \log (5)\right )}{25 \log (5)} \, dx=- x - \frac {e^{\frac {2 x^{3} \log {\left (5 \right )} + x e^{x}}{\log {\left (5 \right )}}}}{25} \]
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Time = 0.34 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.15 \[ \int \frac {-25 \log (5)+e^{\frac {e^x x+2 x^3 \log (5)}{\log (5)}} \left (e^x (-1-x)-6 x^2 \log (5)\right )}{25 \log (5)} \, dx=-\frac {25 \, x \log \left (5\right ) + e^{\left (2 \, x^{3} + \frac {x e^{x}}{\log \left (5\right )}\right )} \log \left (5\right )}{25 \, \log \left (5\right )} \]
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Time = 0.28 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.15 \[ \int \frac {-25 \log (5)+e^{\frac {e^x x+2 x^3 \log (5)}{\log (5)}} \left (e^x (-1-x)-6 x^2 \log (5)\right )}{25 \log (5)} \, dx=-\frac {25 \, x \log \left (5\right ) + e^{\left (2 \, x^{3} + \frac {x e^{x}}{\log \left (5\right )}\right )} \log \left (5\right )}{25 \, \log \left (5\right )} \]
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Time = 0.13 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.81 \[ \int \frac {-25 \log (5)+e^{\frac {e^x x+2 x^3 \log (5)}{\log (5)}} \left (e^x (-1-x)-6 x^2 \log (5)\right )}{25 \log (5)} \, dx=-x-\frac {{\mathrm {e}}^{2\,x^3}\,{\mathrm {e}}^{\frac {x\,{\mathrm {e}}^x}{\ln \left (5\right )}}}{25} \]
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