Optimal. Leaf size=24 \[ -3+\frac {3^{3+\frac {2}{5+x+x^2-\log (x)}}}{x^6} \]
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Rubi [B] time = 0.26, antiderivative size = 104, normalized size of antiderivative = 4.33, number of steps used = 1, number of rules used = 1, integrand size = 124, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.008, Rules used = {2288} \begin {gather*} -\frac {\left (-2 x^2-x+1\right ) 3^{\frac {2}{x^2+x-\log (x)+5}+3} \left (x^2+x-\log (x)+5\right )^2}{\left (2 x-\frac {1}{x}+1\right ) \left (x^{11}+2 x^{10}+11 x^9+10 x^8+25 x^7+x^7 \log ^2(x)-2 \left (x^9+x^8+5 x^7\right ) \log (x)\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {3^{3+\frac {2}{5+x+x^2-\log (x)}} \left (1-x-2 x^2\right ) \left (5+x+x^2-\log (x)\right )^2}{\left (1-\frac {1}{x}+2 x\right ) \left (25 x^7+10 x^8+11 x^9+2 x^{10}+x^{11}-2 \left (5 x^7+x^8+x^9\right ) \log (x)+x^7 \log ^2(x)\right )}\\ \end {aligned} \end {gather*}
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Mathematica [F] time = 3.50, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {3^{-\frac {2}{-5-x-x^2+\log (x)}} \left (-4050-1620 x-1782 x^2-324 x^3-162 x^4+\left (54-54 x-108 x^2\right ) \log (3)+\left (1620+324 x+324 x^2\right ) \log (x)-162 \log ^2(x)\right )}{25 x^7+10 x^8+11 x^9+2 x^{10}+x^{11}+\left (-10 x^7-2 x^8-2 x^9\right ) \log (x)+x^7 \log ^2(x)} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.53, size = 21, normalized size = 0.88 \begin {gather*} \frac {27 \cdot 3^{\frac {2}{x^{2} + x - \log \relax (x) + 5}}}{x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {54 \, {\left (3 \, x^{4} + 6 \, x^{3} + 33 \, x^{2} + {\left (2 \, x^{2} + x - 1\right )} \log \relax (3) - 6 \, {\left (x^{2} + x + 5\right )} \log \relax (x) + 3 \, \log \relax (x)^{2} + 30 \, x + 75\right )} 3^{\frac {2}{x^{2} + x - \log \relax (x) + 5}}}{x^{11} + 2 \, x^{10} + 11 \, x^{9} + x^{7} \log \relax (x)^{2} + 10 \, x^{8} + 25 \, x^{7} - 2 \, {\left (x^{9} + x^{8} + 5 \, x^{7}\right )} \log \relax (x)}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 24, normalized size = 1.00
method | result | size |
risch | \(\frac {27 \,3^{-\frac {2}{\ln \relax (x )-x^{2}-x -5}}}{x^{6}}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} -\frac {27 \cdot 3^{\frac {2}{x^{2} + x - \log \relax (x) + 5}} \log \relax (3)}{2 \, x^{8} \log \relax (3) + x^{7} \log \relax (3) - x^{6} \log \relax (3)} + \frac {27 \cdot 3^{\frac {2}{x^{2} + x - \log \relax (x) + 5}} \log \relax (3)}{2 \, x^{7} \log \relax (3) + x^{6} \log \relax (3) - x^{5} \log \relax (3)} + \frac {54 \cdot 3^{\frac {2}{x^{2} + x - \log \relax (x) + 5}} \log \relax (3)}{2 \, x^{6} \log \relax (3) + x^{5} \log \relax (3) - x^{4} \log \relax (3)} + \frac {2025 \cdot 3^{\frac {2}{x^{2} + x - \log \relax (x) + 5}}}{2 \, x^{8} \log \relax (3) + x^{7} \log \relax (3) - x^{6} \log \relax (3)} + \frac {810 \cdot 3^{\frac {2}{x^{2} + x - \log \relax (x) + 5}}}{2 \, x^{7} \log \relax (3) + x^{6} \log \relax (3) - x^{5} \log \relax (3)} + \frac {891 \cdot 3^{\frac {2}{x^{2} + x - \log \relax (x) + 5}}}{2 \, x^{6} \log \relax (3) + x^{5} \log \relax (3) - x^{4} \log \relax (3)} + \frac {162 \cdot 3^{\frac {2}{x^{2} + x - \log \relax (x) + 5}}}{2 \, x^{5} \log \relax (3) + x^{4} \log \relax (3) - x^{3} \log \relax (3)} + \frac {81 \cdot 3^{\frac {2}{x^{2} + x - \log \relax (x) + 5}}}{2 \, x^{4} \log \relax (3) + x^{3} \log \relax (3) - x^{2} \log \relax (3)} - 2 \, \int -\frac {81 \, {\left (2 \, {\left (x^{2} + x + 5\right )} \log \relax (x) - \log \relax (x)^{2}\right )} 3^{\frac {2}{x^{2} + x - \log \relax (x) + 5}}}{x^{11} + 2 \, x^{10} + 11 \, x^{9} + x^{7} \log \relax (x)^{2} + 10 \, x^{8} + 25 \, x^{7} - 2 \, {\left (x^{9} + x^{8} + 5 \, x^{7}\right )} \log \relax (x)}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 6.62, size = 21, normalized size = 0.88 \begin {gather*} \frac {27\,3^{\frac {2}{x-\ln \relax (x)+x^2+5}}}{x^6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.64, size = 20, normalized size = 0.83 \begin {gather*} \frac {27 e^{- \frac {2 \log {\relax (3 )}}{- x^{2} - x + \log {\relax (x )} - 5}}}{x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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