Optimal. Leaf size=22 \[ \frac {5+2 x}{e^{27/2} \left (3+x^2-\log (x)\right )} \]
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Rubi [F] time = 0.69, 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 {5+8 x-10 x^2-2 x^3-2 x \log (x)}{e^{27/2} \left (9 x+6 x^3+x^5\right )+e^{27/2} \left (-6 x-2 x^3\right ) \log (x)+e^{27/2} x \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 {5+8 x-10 x^2-2 x^3-2 x \log (x)}{e^{27/2} x \left (3+x^2-\log (x)\right )^2} \, dx\\ &=\frac {\int \frac {5+8 x-10 x^2-2 x^3-2 x \log (x)}{x \left (3+x^2-\log (x)\right )^2} \, dx}{e^{27/2}}\\ &=\frac {\int \left (\frac {5+2 x-10 x^2-4 x^3}{x \left (3+x^2-\log (x)\right )^2}+\frac {2}{3+x^2-\log (x)}\right ) \, dx}{e^{27/2}}\\ &=\frac {\int \frac {5+2 x-10 x^2-4 x^3}{x \left (3+x^2-\log (x)\right )^2} \, dx}{e^{27/2}}+\frac {2 \int \frac {1}{3+x^2-\log (x)} \, dx}{e^{27/2}}\\ &=\frac {\int \left (\frac {2}{\left (3+x^2-\log (x)\right )^2}+\frac {5}{x \left (3+x^2-\log (x)\right )^2}-\frac {10 x}{\left (3+x^2-\log (x)\right )^2}-\frac {4 x^2}{\left (3+x^2-\log (x)\right )^2}\right ) \, dx}{e^{27/2}}+\frac {2 \int \frac {1}{3+x^2-\log (x)} \, dx}{e^{27/2}}\\ &=\frac {2 \int \frac {1}{\left (3+x^2-\log (x)\right )^2} \, dx}{e^{27/2}}+\frac {2 \int \frac {1}{3+x^2-\log (x)} \, dx}{e^{27/2}}-\frac {4 \int \frac {x^2}{\left (3+x^2-\log (x)\right )^2} \, dx}{e^{27/2}}+\frac {5 \int \frac {1}{x \left (3+x^2-\log (x)\right )^2} \, dx}{e^{27/2}}-\frac {10 \int \frac {x}{\left (3+x^2-\log (x)\right )^2} \, dx}{e^{27/2}}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.29, size = 22, normalized size = 1.00 \begin {gather*} \frac {-5-2 x}{e^{27/2} \left (-3-x^2+\log (x)\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.49, size = 23, normalized size = 1.05 \begin {gather*} \frac {2 \, x + 5}{{\left (x^{2} + 3\right )} e^{\frac {27}{2}} - e^{\frac {27}{2}} \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.36, size = 22, normalized size = 1.00 \begin {gather*} \frac {2 \, x e^{\left (-\frac {27}{2}\right )} + 5 \, e^{\left (-\frac {27}{2}\right )}}{x^{2} - \log \relax (x) + 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.15, size = 20, normalized size = 0.91
method | result | size |
risch | \(\frac {\left (5+2 x \right ) {\mathrm e}^{-\frac {27}{2}}}{3-\ln \relax (x )+x^{2}}\) | \(20\) |
norman | \(\frac {2 \,{\mathrm e}^{-\frac {27}{2}} x +5 \,{\mathrm e}^{-\frac {27}{2}}}{3-\ln \relax (x )+x^{2}}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.72, size = 25, normalized size = 1.14 \begin {gather*} \frac {2 \, x + 5}{x^{2} e^{\frac {27}{2}} - e^{\frac {27}{2}} \log \relax (x) + 3 \, e^{\frac {27}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.79, size = 35, normalized size = 1.59 \begin {gather*} \frac {\frac {{\mathrm {e}}^{-\frac {27}{2}}\,\left (6\,x-5\,x^2\right )}{3}+\frac {5\,{\mathrm {e}}^{-\frac {27}{2}}\,\left (x^2+3\right )}{3}}{x^2-\ln \relax (x)+3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 29, normalized size = 1.32 \begin {gather*} \frac {- 2 x - 5}{- x^{2} e^{\frac {27}{2}} + e^{\frac {27}{2}} \log {\relax (x )} - 3 e^{\frac {27}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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