Optimal. Leaf size=28 \[ \frac {-2 e^5+x}{3+x}+\frac {x}{-e^4+x \log (x)} \]
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Rubi [F] time = 0.56, 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 {3 e^8+2 e^{13}-9 x-6 x^2-x^3+e^4 \left (-9-6 x-x^2\right )+\left (-6 e^4 x-4 e^9 x\right ) \log (x)+\left (3 x^2+2 e^5 x^2\right ) \log ^2(x)}{e^8 \left (9+6 x+x^2\right )+e^4 \left (-18 x-12 x^2-2 x^3\right ) \log (x)+\left (9 x^2+6 x^3+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 {3 e^8 \left (1+\frac {2 e^5}{3}\right )-e^4 (3+x)^2-x (3+x)^2-2 e^4 \left (3+2 e^5\right ) x \log (x)+\left (3+2 e^5\right ) x^2 \log ^2(x)}{(3+x)^2 \left (e^4-x \log (x)\right )^2} \, dx\\ &=\int \left (\frac {3+2 e^5}{(3+x)^2}+\frac {-e^4-x}{\left (e^4-x \log (x)\right )^2}\right ) \, dx\\ &=-\frac {3+2 e^5}{3+x}+\int \frac {-e^4-x}{\left (e^4-x \log (x)\right )^2} \, dx\\ &=-\frac {3+2 e^5}{3+x}+\int \left (-\frac {e^4}{\left (e^4-x \log (x)\right )^2}-\frac {x}{\left (e^4-x \log (x)\right )^2}\right ) \, dx\\ &=-\frac {3+2 e^5}{3+x}-e^4 \int \frac {1}{\left (e^4-x \log (x)\right )^2} \, dx-\int \frac {x}{\left (e^4-x \log (x)\right )^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.26, size = 28, normalized size = 1.00 \begin {gather*} \frac {-3-2 e^5}{3+x}+\frac {x}{-e^4+x \log (x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.21, size = 50, normalized size = 1.79 \begin {gather*} -\frac {x^{2} - {\left (2 \, x e^{5} + 3 \, x\right )} \log \relax (x) + 3 \, x + 2 \, e^{9} + 3 \, e^{4}}{{\left (x + 3\right )} e^{4} - {\left (x^{2} + 3 \, x\right )} \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.19, size = 54, normalized size = 1.93 \begin {gather*} -\frac {2 \, x e^{5} \log \relax (x) - x^{2} + 3 \, x \log \relax (x) - 3 \, x - 2 \, e^{9} - 3 \, e^{4}}{x^{2} \log \relax (x) - x e^{4} + 3 \, x \log \relax (x) - 3 \, e^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.18, size = 31, normalized size = 1.11
method | result | size |
risch | \(-\frac {2 \,{\mathrm e}^{5}}{3+x}-\frac {3}{3+x}-\frac {x}{-x \ln \relax (x )+{\mathrm e}^{4}}\) | \(31\) |
norman | \(\frac {-3 x +\left (3+2 \,{\mathrm e}^{5}\right ) x \ln \relax (x )-x^{2}-2 \,{\mathrm e}^{4} {\mathrm e}^{5}-3 \,{\mathrm e}^{4}}{\left (3+x \right ) \left (-x \ln \relax (x )+{\mathrm e}^{4}\right )}\) | \(46\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 50, normalized size = 1.79 \begin {gather*} \frac {x {\left (2 \, e^{5} + 3\right )} \log \relax (x) - x^{2} - 3 \, x - 2 \, e^{9} - 3 \, e^{4}}{x e^{4} - {\left (x^{2} + 3 \, x\right )} \log \relax (x) + 3 \, e^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.41, size = 26, normalized size = 0.93 \begin {gather*} \frac {1}{\ln \relax (x)-\frac {{\mathrm {e}}^4}{x}}-\frac {2\,{\mathrm {e}}^5+3}{x+3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 19, normalized size = 0.68 \begin {gather*} \frac {x}{x \log {\relax (x )} - e^{4}} - \frac {3 + 2 e^{5}}{x + 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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