Optimal. Leaf size=29 \[ \frac {4 \left (-1+\frac {5 \left (4+\frac {3}{x}\right )+\frac {3}{x}}{e^5}\right )}{x+\log (2)} \]
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Rubi [A] time = 0.06, antiderivative size = 40, normalized size of antiderivative = 1.38, number of steps used = 6, number of rules used = 5, integrand size = 53, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.094, Rules used = {6, 1594, 27, 12, 893} \begin {gather*} \frac {72}{e^5 x \log (2)}-\frac {4 \left (18-20 \log (2)+e^5 \log (2)\right )}{e^5 \log (2) (x+\log (2))} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 27
Rule 893
Rule 1594
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-144 x+\left (-80+4 e^5\right ) x^2-72 \log (2)}{e^5 x^4+2 e^5 x^3 \log (2)+e^5 x^2 \log ^2(2)} \, dx\\ &=\int \frac {-144 x+\left (-80+4 e^5\right ) x^2-72 \log (2)}{x^2 \left (e^5 x^2+2 e^5 x \log (2)+e^5 \log ^2(2)\right )} \, dx\\ &=\int \frac {-144 x+\left (-80+4 e^5\right ) x^2-72 \log (2)}{e^5 x^2 (x+\log (2))^2} \, dx\\ &=\frac {\int \frac {-144 x+\left (-80+4 e^5\right ) x^2-72 \log (2)}{x^2 (x+\log (2))^2} \, dx}{e^5}\\ &=\frac {\int \left (-\frac {72}{x^2 \log (2)}+\frac {4 \left (18-20 \log (2)+e^5 \log (2)\right )}{\log (2) (x+\log (2))^2}\right ) \, dx}{e^5}\\ &=\frac {72}{e^5 x \log (2)}-\frac {4 \left (18-20 \log (2)+e^5 \log (2)\right )}{e^5 \log (2) (x+\log (2))}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 26, normalized size = 0.90 \begin {gather*} \frac {4 \left (18+20 x-e^5 x\right )}{e^5 \left (x^2+x \log (2)\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.84, size = 26, normalized size = 0.90 \begin {gather*} -\frac {4 \, {\left (x e^{5} - 20 \, x - 18\right )}}{x^{2} e^{5} + x e^{5} \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 23, normalized size = 0.79 \begin {gather*} -\frac {4 \, {\left (x e^{5} - 20 \, x - 18\right )} e^{\left (-5\right )}}{x^{2} + x \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 23, normalized size = 0.79
method | result | size |
risch | \(\frac {\left (\left (-4 \,{\mathrm e}^{5}+80\right ) x +72\right ) {\mathrm e}^{-5}}{x \left (\ln \relax (2)+x \right )}\) | \(23\) |
gosper | \(-\frac {4 \left (x \,{\mathrm e}^{5}-20 x -18\right ) {\mathrm e}^{-5}}{x \left (\ln \relax (2)+x \right )}\) | \(25\) |
norman | \(\frac {-4 \left ({\mathrm e}^{5}-20\right ) {\mathrm e}^{-5} x +72 \,{\mathrm e}^{-5}}{x \left (\ln \relax (2)+x \right )}\) | \(29\) |
default | \(4 \,{\mathrm e}^{-5} \left (-\frac {{\mathrm e}^{5} \ln \relax (2)-20 \ln \relax (2)+18}{\ln \relax (2) \left (\ln \relax (2)+x \right )}+\frac {18}{x \ln \relax (2)}\right )\) | \(40\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 25, normalized size = 0.86 \begin {gather*} -\frac {4 \, {\left (x {\left (e^{5} - 20\right )} - 18\right )}}{x^{2} e^{5} + x e^{5} \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.96, size = 23, normalized size = 0.79 \begin {gather*} \frac {4\,{\mathrm {e}}^{-5}\,\left (20\,x-x\,{\mathrm {e}}^5+18\right )}{x\,\left (x+\ln \relax (2)\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.65, size = 26, normalized size = 0.90 \begin {gather*} - \frac {x \left (-80 + 4 e^{5}\right ) - 72}{x^{2} e^{5} + x e^{5} \log {\relax (2 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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