Integrand size = 73, antiderivative size = 18 \[ \int \frac {e^{-\frac {75}{x^2+x^5-x \log (2)}} \left (150 x+375 x^4-75 \log (2)\right )}{x^4+x^{10}-2 x^3 \log (2)+x^2 \log ^2(2)+x^4 \left (2 x^3-2 x^2 \log (2)\right )} \, dx=e^{-\frac {75}{x \left (x+x^4-\log (2)\right )}} \]
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Time = 0.47 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.041, Rules used = {6820, 12, 6838} \[ \int \frac {e^{-\frac {75}{x^2+x^5-x \log (2)}} \left (150 x+375 x^4-75 \log (2)\right )}{x^4+x^{10}-2 x^3 \log (2)+x^2 \log ^2(2)+x^4 \left (2 x^3-2 x^2 \log (2)\right )} \, dx=e^{-\frac {75}{x \left (x^4+x-\log (2)\right )}} \]
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Rule 12
Rule 6820
Rule 6838
Rubi steps \begin{align*} \text {integral}& = \int \frac {75 e^{-\frac {75}{x \left (x+x^4-\log (2)\right )}} \left (2 x+5 x^4-\log (2)\right )}{x^2 \left (x+x^4-\log (2)\right )^2} \, dx \\ & = 75 \int \frac {e^{-\frac {75}{x \left (x+x^4-\log (2)\right )}} \left (2 x+5 x^4-\log (2)\right )}{x^2 \left (x+x^4-\log (2)\right )^2} \, dx \\ & = e^{-\frac {75}{x \left (x+x^4-\log (2)\right )}} \\ \end{align*}
Time = 0.58 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int \frac {e^{-\frac {75}{x^2+x^5-x \log (2)}} \left (150 x+375 x^4-75 \log (2)\right )}{x^4+x^{10}-2 x^3 \log (2)+x^2 \log ^2(2)+x^4 \left (2 x^3-2 x^2 \log (2)\right )} \, dx=e^{-\frac {75}{x^2+x^5-x \log (2)}} \]
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Time = 5.16 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11
method | result | size |
gosper | \({\mathrm e}^{\frac {75}{x \left (-x^{4}+\ln \left (2\right )-x \right )}}\) | \(20\) |
risch | \({\mathrm e}^{\frac {75}{x \left (-x^{4}+\ln \left (2\right )-x \right )}}\) | \(20\) |
parallelrisch | \({\mathrm e}^{\frac {75}{x \left (-x^{4}+\ln \left (2\right )-x \right )}}\) | \(20\) |
norman | \(\frac {x \ln \left (2\right ) {\mathrm e}^{-\frac {75}{x^{5}-x \ln \left (2\right )+x^{2}}}-x^{2} {\mathrm e}^{-\frac {75}{x^{5}-x \ln \left (2\right )+x^{2}}}-x^{5} {\mathrm e}^{-\frac {75}{x^{5}-x \ln \left (2\right )+x^{2}}}}{x \left (-x^{4}+\ln \left (2\right )-x \right )}\) | \(84\) |
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Time = 0.25 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.94 \[ \int \frac {e^{-\frac {75}{x^2+x^5-x \log (2)}} \left (150 x+375 x^4-75 \log (2)\right )}{x^4+x^{10}-2 x^3 \log (2)+x^2 \log ^2(2)+x^4 \left (2 x^3-2 x^2 \log (2)\right )} \, dx=e^{\left (-\frac {75}{x^{5} + x^{2} - x \log \left (2\right )}\right )} \]
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Time = 0.55 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.83 \[ \int \frac {e^{-\frac {75}{x^2+x^5-x \log (2)}} \left (150 x+375 x^4-75 \log (2)\right )}{x^4+x^{10}-2 x^3 \log (2)+x^2 \log ^2(2)+x^4 \left (2 x^3-2 x^2 \log (2)\right )} \, dx=e^{- \frac {75}{x^{5} + x^{2} - x \log {\left (2 \right )}}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 56 vs. \(2 (17) = 34\).
Time = 0.37 (sec) , antiderivative size = 56, normalized size of antiderivative = 3.11 \[ \int \frac {e^{-\frac {75}{x^2+x^5-x \log (2)}} \left (150 x+375 x^4-75 \log (2)\right )}{x^4+x^{10}-2 x^3 \log (2)+x^2 \log ^2(2)+x^4 \left (2 x^3-2 x^2 \log (2)\right )} \, dx=e^{\left (-\frac {75 \, x^{3}}{x^{4} \log \left (2\right ) + x \log \left (2\right ) - \log \left (2\right )^{2}} - \frac {75}{x^{4} \log \left (2\right ) + x \log \left (2\right ) - \log \left (2\right )^{2}} + \frac {75}{x \log \left (2\right )}\right )} \]
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Time = 0.25 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.94 \[ \int \frac {e^{-\frac {75}{x^2+x^5-x \log (2)}} \left (150 x+375 x^4-75 \log (2)\right )}{x^4+x^{10}-2 x^3 \log (2)+x^2 \log ^2(2)+x^4 \left (2 x^3-2 x^2 \log (2)\right )} \, dx=e^{\left (-\frac {75}{x^{5} + x^{2} - x \log \left (2\right )}\right )} \]
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Time = 10.58 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.94 \[ \int \frac {e^{-\frac {75}{x^2+x^5-x \log (2)}} \left (150 x+375 x^4-75 \log (2)\right )}{x^4+x^{10}-2 x^3 \log (2)+x^2 \log ^2(2)+x^4 \left (2 x^3-2 x^2 \log (2)\right )} \, dx={\mathrm {e}}^{-\frac {75}{x^5+x^2-\ln \left (2\right )\,x}} \]
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