Optimal. Leaf size=28 \[ \frac {e^{3+e^5}}{\left (-x+\frac {3}{4} (3-x) x\right ) \log (x)} \]
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Rubi [F] time = 1.02, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {e^{3+e^5} (-20+12 x)+e^{3+e^5} (-20+24 x) \log (x)}{\left (25 x^2-30 x^3+9 x^4\right ) \log ^2(x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{3+e^5} (-20+12 x)+e^{3+e^5} (-20+24 x) \log (x)}{x^2 \left (25-30 x+9 x^2\right ) \log ^2(x)} \, dx\\ &=\int \frac {e^{3+e^5} (-20+12 x)+e^{3+e^5} (-20+24 x) \log (x)}{x^2 (-5+3 x)^2 \log ^2(x)} \, dx\\ &=\int \frac {4 e^{3+e^5} (-5+3 x-5 \log (x)+6 x \log (x))}{(5-3 x)^2 x^2 \log ^2(x)} \, dx\\ &=\left (4 e^{3+e^5}\right ) \int \frac {-5+3 x-5 \log (x)+6 x \log (x)}{(5-3 x)^2 x^2 \log ^2(x)} \, dx\\ &=\left (4 e^{3+e^5}\right ) \int \left (\frac {1}{x^2 (-5+3 x) \log ^2(x)}+\frac {-5+6 x}{x^2 (-5+3 x)^2 \log (x)}\right ) \, dx\\ &=\left (4 e^{3+e^5}\right ) \int \frac {1}{x^2 (-5+3 x) \log ^2(x)} \, dx+\left (4 e^{3+e^5}\right ) \int \frac {-5+6 x}{x^2 (-5+3 x)^2 \log (x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.10, size = 23, normalized size = 0.82 \begin {gather*} -\frac {4 e^{3+e^5}}{x (-5+3 x) \log (x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.66, size = 22, normalized size = 0.79 \begin {gather*} -\frac {4 \, e^{\left (e^{5} + 3\right )}}{{\left (3 \, x^{2} - 5 \, x\right )} \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.12, size = 22, normalized size = 0.79 \begin {gather*} -\frac {4 \, e^{\left (e^{5} + 3\right )}}{3 \, x^{2} \log \relax (x) - 5 \, x \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 22, normalized size = 0.79
method | result | size |
norman | \(-\frac {4 \,{\mathrm e}^{3} {\mathrm e}^{{\mathrm e}^{5}}}{x \left (3 x -5\right ) \ln \relax (x )}\) | \(22\) |
risch | \(-\frac {4 \,{\mathrm e}^{3+{\mathrm e}^{5}}}{\ln \relax (x ) \left (3 x -5\right ) x}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.39, size = 22, normalized size = 0.79 \begin {gather*} -\frac {4 \, e^{\left (e^{5} + 3\right )}}{{\left (3 \, x^{2} - 5 \, x\right )} \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.23, size = 33, normalized size = 1.18 \begin {gather*} \frac {4\,{\mathrm {e}}^{{\mathrm {e}}^5+3}}{5\,x\,\ln \relax (x)}-\frac {12\,{\mathrm {e}}^{{\mathrm {e}}^5+3}}{5\,\ln \relax (x)\,\left (3\,x-5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 22, normalized size = 0.79 \begin {gather*} - \frac {4 e^{3} e^{e^{5}}}{\left (3 x^{2} - 5 x\right ) \log {\relax (x )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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