Optimal. Leaf size=27 \[ e^{\left (6+\frac {5-x-\log (3)-\frac {12}{\log (x)}}{x}\right )^2}+x \]
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Rubi [F]
time = 40.94, 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 {x^3 \log ^3(x)+\exp \left (\frac {144+(-120-120 x+24 \log (3)) \log (x)+\left (25+50 x+25 x^2+(-10-10 x) \log (3)+\log ^2(3)\right ) \log ^2(x)}{x^2 \log ^2(x)}\right ) \left (-288+(-168+120 x-24 \log (3)) \log (x)+(240+120 x-48 \log (3)) \log ^2(x)+\left (-50-50 x+(20+10 x) \log (3)-2 \log ^2(3)\right ) \log ^3(x)\right )}{x^3 \log ^3(x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1+\frac {2\ 3^{-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (25+\frac {50}{x}+\frac {25 \left (1+\frac {\log ^2(3)}{25}\right )}{x^2}+\frac {144}{x^2 \log ^2(x)}-\frac {120}{x^2 \log (x)}-\frac {120}{x \log (x)}\right ) \left (12-5 x \log (x)-5 \left (1-\frac {\log (3)}{5}\right ) \log (x)\right ) \left (-12-12 \log (x)+5 \left (1-\frac {\log (3)}{5}\right ) \log ^2(x)\right )}{x^3 \log ^3(x)}\right ) \, dx\\ &=x+2 \int \frac {3^{-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (25+\frac {50}{x}+\frac {25 \left (1+\frac {\log ^2(3)}{25}\right )}{x^2}+\frac {144}{x^2 \log ^2(x)}-\frac {120}{x^2 \log (x)}-\frac {120}{x \log (x)}\right ) \left (12-5 x \log (x)-5 \left (1-\frac {\log (3)}{5}\right ) \log (x)\right ) \left (-12-12 \log (x)+5 \left (1-\frac {\log (3)}{5}\right ) \log ^2(x)\right )}{x^3 \log ^3(x)} \, dx\\ &=x+2 \int \frac {3^{-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right ) \left (12-5 x \log (x)-5 \left (1-\frac {\log (3)}{5}\right ) \log (x)\right ) \left (-12-12 \log (x)+5 \left (1-\frac {\log (3)}{5}\right ) \log ^2(x)\right )}{x^3 \log ^3(x)} \, dx\\ &=x+2 \int \left (\frac {3^{-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right ) (5+5 x-\log (3)) (-5+\log (3))}{x^3}-\frac {16\ 3^{2-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right )}{x^3 \log ^3(x)}+\frac {4\ 3^{1-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right ) (-7+5 x-\log (3))}{x^3 \log ^2(x)}+\frac {4\ 3^{1-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right ) (10+5 x-\log (9))}{x^3 \log (x)}\right ) \, dx\\ &=x+8 \int \frac {3^{1-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right ) (-7+5 x-\log (3))}{x^3 \log ^2(x)} \, dx+8 \int \frac {3^{1-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right ) (10+5 x-\log (9))}{x^3 \log (x)} \, dx-32 \int \frac {3^{2-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right )}{x^3 \log ^3(x)} \, dx+(2 (-5+\log (3))) \int \frac {3^{-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right ) (5+5 x-\log (3))}{x^3} \, dx\\ &=x+8 \int \left (\frac {5\ 3^{1-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right )}{x^2 \log ^2(x)}+\frac {3^{1-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right ) (-7-\log (3))}{x^3 \log ^2(x)}\right ) \, dx+8 \int \left (\frac {5\ 3^{1-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right )}{x^2 \log (x)}+\frac {3^{1-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right ) (10-\log (9))}{x^3 \log (x)}\right ) \, dx-32 \int \frac {3^{2-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right )}{x^3 \log ^3(x)} \, dx+(2 (-5+\log (3))) \int \left (\frac {5\ 3^{-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right )}{x^2}+\frac {3^{-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right ) (5-\log (3))}{x^3}\right ) \, dx\\ &=x-32 \int \frac {3^{2-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right )}{x^3 \log ^3(x)} \, dx+40 \int \frac {3^{1-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right )}{x^2 \log ^2(x)} \, dx+40 \int \frac {3^{1-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right )}{x^2 \log (x)} \, dx-(10 (5-\log (3))) \int \frac {3^{-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right )}{x^2} \, dx-\left (2 (5-\log (3))^2\right ) \int \frac {3^{-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right )}{x^3} \, dx-(8 (7+\log (3))) \int \frac {3^{1-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right )}{x^3 \log ^2(x)} \, dx+(8 (10-\log (9))) \int \frac {3^{1-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right )}{x^3 \log (x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(65\) vs. \(2(27)=54\).
time = 0.24, size = 65, normalized size = 2.41 \begin {gather*} 3^{-\frac {10}{x^2}-\frac {10}{x}+\frac {24}{x^2 \log (x)}} e^{25+\frac {50}{x}+\frac {25+\log ^2(3)}{x^2}+\frac {144}{x^2 \log ^2(x)}-\frac {120 (1+x)}{x^2 \log (x)}}+x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.29, size = 30, normalized size = 1.11
method | result | size |
risch | \(x +{\mathrm e}^{\frac {\left (\ln \left (3\right ) \ln \left (x \right )-5 x \ln \left (x \right )-5 \ln \left (x \right )+12\right )^{2}}{\ln \left (x \right )^{2} x^{2}}}\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 75 vs.
\(2 (22) = 44\).
time = 0.69, size = 75, normalized size = 2.78 \begin {gather*} x + e^{\left (-\frac {10 \, \log \left (3\right )}{x} + \frac {\log \left (3\right )^{2}}{x^{2}} + \frac {50}{x} - \frac {10 \, \log \left (3\right )}{x^{2}} + \frac {25}{x^{2}} - \frac {120}{x \log \left (x\right )} + \frac {24 \, \log \left (3\right )}{x^{2} \log \left (x\right )} - \frac {120}{x^{2} \log \left (x\right )} + \frac {144}{x^{2} \log \left (x\right )^{2}} + 25\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 52 vs.
\(2 (22) = 44\).
time = 0.45, size = 52, normalized size = 1.93 \begin {gather*} x + e^{\left (\frac {{\left (25 \, x^{2} - 10 \, {\left (x + 1\right )} \log \left (3\right ) + \log \left (3\right )^{2} + 50 \, x + 25\right )} \log \left (x\right )^{2} - 24 \, {\left (5 \, x - \log \left (3\right ) + 5\right )} \log \left (x\right ) + 144}{x^{2} \log \left (x\right )^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 56 vs.
\(2 (19) = 38\).
time = 0.42, size = 56, normalized size = 2.07 \begin {gather*} x + e^{\frac {\left (- 120 x - 120 + 24 \log {\left (3 \right )}\right ) \log {\left (x \right )} + \left (25 x^{2} + 50 x + \left (- 10 x - 10\right ) \log {\left (3 \right )} + \log {\left (3 \right )}^{2} + 25\right ) \log {\left (x \right )}^{2} + 144}{x^{2} \log {\left (x \right )}^{2}}} \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*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.67, size = 85, normalized size = 3.15 \begin {gather*} x+\frac {3^{\frac {24}{x^2\,\ln \left (x\right )}}\,{\mathrm {e}}^{25}\,{\mathrm {e}}^{\frac {{\ln \left (3\right )}^2}{x^2}}\,{\mathrm {e}}^{\frac {25}{x^2}}\,{\mathrm {e}}^{50/x}\,{\mathrm {e}}^{-\frac {120}{x\,\ln \left (x\right )}}\,{\mathrm {e}}^{-\frac {120}{x^2\,\ln \left (x\right )}}\,{\mathrm {e}}^{\frac {144}{x^2\,{\ln \left (x\right )}^2}}}{3^{10/x}\,3^{\frac {10}{x^2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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