Optimal. Leaf size=24 \[ (-3+x) \left (-e^{\frac {1-\frac {1}{\log (25)}}{x^2}}+2 x\right ) \]
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Rubi [A] time = 0.13, antiderivative size = 32, normalized size of antiderivative = 1.33, number of steps used = 4, number of rules used = 3, integrand size = 56, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.054, Rules used = {12, 14, 2288} \begin {gather*} (3-x) e^{\frac {1-\frac {1}{\log (25)}}{x^2}}+\frac {1}{2} (3-2 x)^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {\left (-6 x^3+4 x^4\right ) \log (25)+e^{\frac {-1+\log (25)}{x^2 \log (25)}} \left (6-2 x+\left (-6+2 x-x^3\right ) \log (25)\right )}{x^3} \, dx}{\log (25)}\\ &=\frac {\int \left (2 (-3+2 x) \log (25)+\frac {e^{\frac {1-\frac {1}{\log (25)}}{x^2}} \left (6 (1-\log (25))-2 x (1-\log (25))-x^3 \log (25)\right )}{x^3}\right ) \, dx}{\log (25)}\\ &=\frac {1}{2} (3-2 x)^2+\frac {\int \frac {e^{\frac {1-\frac {1}{\log (25)}}{x^2}} \left (6 (1-\log (25))-2 x (1-\log (25))-x^3 \log (25)\right )}{x^3} \, dx}{\log (25)}\\ &=\frac {1}{2} (3-2 x)^2+e^{\frac {1-\frac {1}{\log (25)}}{x^2}} (3-x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.11, size = 47, normalized size = 1.96 \begin {gather*} -6 x+2 x^2-\frac {e^{\frac {-1+\log (25)}{x^2 \log (25)}} (6-6 \log (25)+x (-2+2 \log (25)))}{2 (-1+\log (25))} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.57, size = 30, normalized size = 1.25 \begin {gather*} 2 \, x^{2} - {\left (x - 3\right )} e^{\left (\frac {2 \, \log \relax (5) - 1}{2 \, x^{2} \log \relax (5)}\right )} - 6 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.26, size = 59, normalized size = 2.46 \begin {gather*} \frac {2 \, x^{2} \log \relax (5) - x e^{\left (\frac {2 \, \log \relax (5) - 1}{2 \, x^{2} \log \relax (5)}\right )} \log \relax (5) - 6 \, x \log \relax (5) + 3 \, e^{\left (\frac {2 \, \log \relax (5) - 1}{2 \, x^{2} \log \relax (5)}\right )} \log \relax (5)}{\log \relax (5)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.23, size = 42, normalized size = 1.75
method | result | size |
risch | \(2 x^{2}-6 x +\frac {\left (-2 x \ln \relax (5)+6 \ln \relax (5)\right ) {\mathrm e}^{\frac {2 \ln \relax (5)-1}{2 x^{2} \ln \relax (5)}}}{2 \ln \relax (5)}\) | \(42\) |
norman | \(\frac {-6 x^{3}+2 x^{4}+3 x^{2} {\mathrm e}^{\frac {2 \ln \relax (5)-1}{2 x^{2} \ln \relax (5)}}-x^{3} {\mathrm e}^{\frac {2 \ln \relax (5)-1}{2 x^{2} \ln \relax (5)}}}{x^{2}}\) | \(58\) |
derivativedivides | \(-\frac {-4 x^{2} \ln \relax (5)+12 x \ln \relax (5)+\frac {3 \,{\mathrm e}^{\frac {1-\frac {1}{2 \ln \relax (5)}}{x^{2}}}}{1-\frac {1}{2 \ln \relax (5)}}-\frac {6 \ln \relax (5) {\mathrm e}^{\frac {1-\frac {1}{2 \ln \relax (5)}}{x^{2}}}}{1-\frac {1}{2 \ln \relax (5)}}+2 \ln \relax (5) x \,{\mathrm e}^{\frac {1-\frac {1}{2 \ln \relax (5)}}{x^{2}}}}{2 \ln \relax (5)}\) | \(90\) |
default | \(\frac {4 x^{2} \ln \relax (5)-12 x \ln \relax (5)-\frac {3 \,{\mathrm e}^{\frac {1-\frac {1}{2 \ln \relax (5)}}{x^{2}}}}{1-\frac {1}{2 \ln \relax (5)}}+\frac {6 \ln \relax (5) {\mathrm e}^{\frac {1-\frac {1}{2 \ln \relax (5)}}{x^{2}}}}{1-\frac {1}{2 \ln \relax (5)}}-2 \ln \relax (5) x \,{\mathrm e}^{\frac {1-\frac {1}{2 \ln \relax (5)}}{x^{2}}}}{2 \ln \relax (5)}\) | \(90\) |
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 {2 \, x^{2} \log \relax (5) - x e^{\left (\frac {2 \, \log \relax (5) - 1}{2 \, x^{2} \log \relax (5)}\right )} \log \relax (5) - 6 \, x \log \relax (5) + 3 \, e^{\left (\frac {2 \, \log \relax (5) - 1}{2 \, x^{2} \log \relax (5)}\right )} \log \relax (5)}{\log \relax (5)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.19, size = 52, normalized size = 2.17 \begin {gather*} \frac {{\mathrm {e}}^{\frac {1}{x^2}-\frac {1}{2\,x^2\,\ln \relax (5)}}\,\ln \left (125\right )}{\ln \relax (5)}-x\,{\mathrm {e}}^{\frac {1}{x^2}-\frac {1}{2\,x^2\,\ln \relax (5)}}-6\,x+\frac {x^2\,\ln \left (25\right )}{\ln \relax (5)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.29, size = 26, normalized size = 1.08 \begin {gather*} 2 x^{2} - 6 x + \left (3 - x\right ) e^{\frac {- \frac {1}{2} + \log {\relax (5 )}}{x^{2} \log {\relax (5 )}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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