Optimal. Leaf size=18 \[ 4 x \log ^{2 e^{5 (5+\log (2))^2}}(x) \]
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Rubi [C] Result contains higher order function than in optimal. Order 4 vs. order 3 in
optimal.
time = 0.08, antiderivative size = 173, normalized size of antiderivative = 9.61, number of steps
used = 4, number of rules used = 5, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {2336, 2212,
2408, 19, 6692} \begin {gather*} 4 (-\log (x))^{-2251799813685248 e^{5 \left (25+\log ^2(2)\right )}} \log ^{1+2251799813685248 e^{5 \left (25+\log ^2(2)\right )}}(x) \text {Gamma}\left (2251799813685248 e^{5 \left (25+\log ^2(2)\right )},-\log (x)\right )+4 (-\log (x))^{-2251799813685248 e^{5 \left (25+\log ^2(2)\right )}} \log ^{2251799813685248 e^{5 \left (25+\log ^2(2)\right )}}(x) \text {Gamma}\left (1+2251799813685248 e^{5 \left (25+\log ^2(2)\right )},-\log (x)\right )-4 (-\log (x))^{-2251799813685248 e^{5 \left (25+\log ^2(2)\right )}} \left (\log (x)+2251799813685248 e^{5 \left (25+\log ^2(2)\right )}\right ) \log ^{2251799813685248 e^{5 \left (25+\log ^2(2)\right )}}(x) \text {Gamma}\left (2251799813685248 e^{5 \left (25+\log ^2(2)\right )},-\log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 19
Rule 2212
Rule 2336
Rule 2408
Rule 6692
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-4 \Gamma \left (2251799813685248 e^{5 \left (25+\log ^2(2)\right )},-\log (x)\right ) (-\log (x))^{-2251799813685248 e^{5 \left (25+\log ^2(2)\right )}} \log ^{2251799813685248 e^{5 \left (25+\log ^2(2)\right )}}(x) \left (2251799813685248 e^{5 \left (25+\log ^2(2)\right )}+\log (x)\right )+4 \int \frac {\Gamma \left (2251799813685248 e^{5 \left (25+\log ^2(2)\right )},-\log (x)\right ) (-\log (x))^{-2251799813685248 e^{5 \left (25+\log ^2(2)\right )}} \log ^{2251799813685248 e^{5 \left (25+\log ^2(2)\right )}}(x)}{x} \, dx\\ &=-4 \Gamma \left (2251799813685248 e^{5 \left (25+\log ^2(2)\right )},-\log (x)\right ) (-\log (x))^{-2251799813685248 e^{5 \left (25+\log ^2(2)\right )}} \log ^{2251799813685248 e^{5 \left (25+\log ^2(2)\right )}}(x) \left (2251799813685248 e^{5 \left (25+\log ^2(2)\right )}+\log (x)\right )+\left (4 (-\log (x))^{-2251799813685248 e^{5 \left (25+\log ^2(2)\right )}} \log ^{2251799813685248 e^{5 \left (25+\log ^2(2)\right )}}(x)\right ) \int \frac {\Gamma \left (2251799813685248 e^{5 \left (25+\log ^2(2)\right )},-\log (x)\right )}{x} \, dx\\ &=-4 \Gamma \left (2251799813685248 e^{5 \left (25+\log ^2(2)\right )},-\log (x)\right ) (-\log (x))^{-2251799813685248 e^{5 \left (25+\log ^2(2)\right )}} \log ^{2251799813685248 e^{5 \left (25+\log ^2(2)\right )}}(x) \left (2251799813685248 e^{5 \left (25+\log ^2(2)\right )}+\log (x)\right )+\left (4 (-\log (x))^{-2251799813685248 e^{5 \left (25+\log ^2(2)\right )}} \log ^{2251799813685248 e^{5 \left (25+\log ^2(2)\right )}}(x)\right ) \text {Subst}\left (\int \Gamma \left (2251799813685248 e^{5 \left (25+\log ^2(2)\right )},-x\right ) \, dx,x,\log (x)\right )\\ &=4 \Gamma \left (1+2251799813685248 e^{5 \left (25+\log ^2(2)\right )},-\log (x)\right ) (-\log (x))^{-2251799813685248 e^{5 \left (25+\log ^2(2)\right )}} \log ^{2251799813685248 e^{5 \left (25+\log ^2(2)\right )}}(x)+4 \Gamma \left (2251799813685248 e^{5 \left (25+\log ^2(2)\right )},-\log (x)\right ) (-\log (x))^{-2251799813685248 e^{5 \left (25+\log ^2(2)\right )}} \log ^{1+2251799813685248 e^{5 \left (25+\log ^2(2)\right )}}(x)-4 \Gamma \left (2251799813685248 e^{5 \left (25+\log ^2(2)\right )},-\log (x)\right ) (-\log (x))^{-2251799813685248 e^{5 \left (25+\log ^2(2)\right )}} \log ^{2251799813685248 e^{5 \left (25+\log ^2(2)\right )}}(x) \left (2251799813685248 e^{5 \left (25+\log ^2(2)\right )}+\log (x)\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 18, normalized size = 1.00 \begin {gather*} 4 x \log ^{2251799813685248 e^{5 \left (25+\log ^2(2)\right )}}(x) \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 180.00, size = 0, normalized size = 0.00 \[\int \frac {\left (4 \ln \left (x \right )+8 \,{\mathrm e}^{5 \ln \left (2\right )^{2}+50 \ln \left (2\right )+125}\right ) {\mathrm e}^{2251799813685248 \,{\mathrm e}^{5 \ln \left (2\right )^{2}+125} \ln \left (\ln \left (x \right )\right )}}{\ln \left (x \right )}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [C] Result contains higher order function than in optimal. Order 4 vs. order
3.
time = 0.50, size = 114, normalized size = 6.33 \begin {gather*} -4 \, \left (-\log \left (x\right )\right )^{-2251799813685248 \, e^{\left (5 \, \log \left (2\right )^{2} + 125\right )} - 1} \log \left (x\right )^{2251799813685248 \, e^{\left (5 \, \log \left (2\right )^{2} + 125\right )} + 1} \Gamma \left (2251799813685248 \, e^{\left (5 \, \log \left (2\right )^{2} + 125\right )} + 1, -\log \left (x\right )\right ) - \frac {9007199254740992 \, \log \left (x\right )^{2251799813685248 \, e^{\left (5 \, \log \left (2\right )^{2} + 125\right )}} e^{\left (5 \, \log \left (2\right )^{2} + 125\right )} \Gamma \left (2251799813685248 \, e^{\left (5 \, \log \left (2\right )^{2} + 125\right )}, -\log \left (x\right )\right )}{\left (-\log \left (x\right )\right )^{2251799813685248 \, e^{\left (5 \, \log \left (2\right )^{2} + 125\right )}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 21, normalized size = 1.17 \begin {gather*} 4 \, x \log \left (x\right )^{2 \, e^{\left (5 \, \log \left (2\right )^{2} + 50 \, \log \left (2\right ) + 125\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. 128 vs.
\(2 (17) = 34\).
time = 2.82, size = 128, normalized size = 7.11 \begin {gather*} \frac {9007199254740992 e^{125} e^{5 \log {\left (2 \right )}^{2}} \log {\left (x \right )}^{-1 + 2251799813685248 e^{125} e^{5 \log {\left (2 \right )}^{2}}} \Gamma \left (2251799813685248 e^{125} e^{5 \log {\left (2 \right )}^{2}}, - \log {\left (x \right )}\right )}{\left (- \log {\left (x \right )}\right )^{-1 + 2251799813685248 e^{125} e^{5 \log {\left (2 \right )}^{2}}}} + \frac {4 \log {\left (x \right )}^{2251799813685248 e^{125} e^{5 \log {\left (2 \right )}^{2}}} \Gamma \left (1 + 2251799813685248 e^{125} e^{5 \log {\left (2 \right )}^{2}}, - \log {\left (x \right )}\right )}{\left (- \log {\left (x \right )}\right )^{2251799813685248 e^{125} e^{5 \log {\left (2 \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 = 0.78, size = 17, normalized size = 0.94 \begin {gather*} 4\,x\,{\ln \left (x\right )}^{2251799813685248\,{\mathrm {e}}^{5\,{\ln \left (2\right )}^2+125}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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