Optimal. Leaf size=32 \[ \frac {1}{16} \left (4-e^{5 \left (6+x^2\right )-\left (2-\log ^2(x)\right )^2}\right )^2 \]
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Rubi [A] time = 0.60, antiderivative size = 53, normalized size of antiderivative = 1.66, number of steps used = 5, number of rules used = 3, integrand size = 84, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.036, Rules used = {12, 14, 6706} \begin {gather*} \frac {1}{16} e^{2 \left (5 x^2-\log ^4(x)+4 \log ^2(x)+26\right )}-\frac {1}{2} e^{5 x^2-\log ^4(x)+4 \log ^2(x)+26} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int \frac {e^{52+10 x^2+8 \log ^2(x)-2 \log ^4(x)} \left (5 x^2+4 \log (x)-2 \log ^3(x)\right )+e^{26+5 x^2+4 \log ^2(x)-\log ^4(x)} \left (-20 x^2-16 \log (x)+8 \log ^3(x)\right )}{x} \, dx\\ &=\frac {1}{4} \int \left (-\frac {4 e^{26+5 x^2+4 \log ^2(x)-\log ^4(x)} \left (5 x^2+4 \log (x)-2 \log ^3(x)\right )}{x}+\frac {e^{2 \left (26+5 x^2+4 \log ^2(x)-\log ^4(x)\right )} \left (5 x^2+4 \log (x)-2 \log ^3(x)\right )}{x}\right ) \, dx\\ &=\frac {1}{4} \int \frac {e^{2 \left (26+5 x^2+4 \log ^2(x)-\log ^4(x)\right )} \left (5 x^2+4 \log (x)-2 \log ^3(x)\right )}{x} \, dx-\int \frac {e^{26+5 x^2+4 \log ^2(x)-\log ^4(x)} \left (5 x^2+4 \log (x)-2 \log ^3(x)\right )}{x} \, dx\\ &=-\frac {1}{2} e^{26+5 x^2+4 \log ^2(x)-\log ^4(x)}+\frac {1}{16} e^{2 \left (26+5 x^2+4 \log ^2(x)-\log ^4(x)\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.70, size = 49, normalized size = 1.53 \begin {gather*} \frac {1}{16} e^{-2 \log ^4(x)} \left (e^{52+10 x^2+8 \log ^2(x)}-8 e^{26+5 x^2+4 \log ^2(x)+\log ^4(x)}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.94, size = 45, normalized size = 1.41 \begin {gather*} -\frac {1}{2} \, e^{\left (-\log \relax (x)^{4} + 5 \, x^{2} + 4 \, \log \relax (x)^{2} + 26\right )} + \frac {1}{16} \, e^{\left (-2 \, \log \relax (x)^{4} + 10 \, x^{2} + 8 \, \log \relax (x)^{2} + 52\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 45, normalized size = 1.41 \begin {gather*} -\frac {1}{2} \, e^{\left (-\log \relax (x)^{4} + 5 \, x^{2} + 4 \, \log \relax (x)^{2} + 26\right )} + \frac {1}{16} \, e^{\left (-2 \, \log \relax (x)^{4} + 10 \, x^{2} + 8 \, \log \relax (x)^{2} + 52\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 46, normalized size = 1.44
method | result | size |
risch | \(\frac {{\mathrm e}^{-2 \ln \relax (x )^{4}+8 \ln \relax (x )^{2}+10 x^{2}+52}}{16}-\frac {{\mathrm e}^{-\ln \relax (x )^{4}+4 \ln \relax (x )^{2}+5 x^{2}+26}}{2}\) | \(46\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 45, normalized size = 1.41 \begin {gather*} -\frac {1}{2} \, e^{\left (-\log \relax (x)^{4} + 5 \, x^{2} + 4 \, \log \relax (x)^{2} + 26\right )} + \frac {1}{16} \, e^{\left (-2 \, \log \relax (x)^{4} + 10 \, x^{2} + 8 \, \log \relax (x)^{2} + 52\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 6.12, size = 49, normalized size = 1.53 \begin {gather*} -\frac {{\mathrm {e}}^{4\,{\ln \relax (x)}^2}\,{\mathrm {e}}^{-2\,{\ln \relax (x)}^4}\,{\mathrm {e}}^{26}\,{\mathrm {e}}^{5\,x^2}\,\left (8\,{\mathrm {e}}^{{\ln \relax (x)}^4}-{\mathrm {e}}^{4\,{\ln \relax (x)}^2}\,{\mathrm {e}}^{26}\,{\mathrm {e}}^{5\,x^2}\right )}{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.36, size = 44, normalized size = 1.38 \begin {gather*} - \frac {e^{5 x^{2} - \log {\relax (x )}^{4} + 4 \log {\relax (x )}^{2} + 26}}{2} + \frac {e^{10 x^{2} - 2 \log {\relax (x )}^{4} + 8 \log {\relax (x )}^{2} + 52}}{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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