Optimal. Leaf size=16 \[ 8 e^{e^{\frac {5}{4 \log ^2\left (x^2\right )}}} \]
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Rubi [A] time = 0.15, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 4, integrand size = 36, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {12, 6715, 2282, 2194} \begin {gather*} 8 e^{e^{\frac {5}{4 \log ^2\left (x^2\right )}}} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2194
Rule 2282
Rule 6715
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (40 \int \frac {e^{e^{\frac {5}{4 \log ^2\left (x^2\right )}}+\frac {5}{4 \log ^2\left (x^2\right )}}}{x \log ^3\left (x^2\right )} \, dx\right )\\ &=-\left (20 \operatorname {Subst}\left (\int \frac {e^{e^{\frac {5}{4 x^2}}+\frac {5}{4 x^2}}}{x^3} \, dx,x,\log \left (x^2\right )\right )\right )\\ &=10 \operatorname {Subst}\left (\int e^{e^{5 x/4}+\frac {5 x}{4}} \, dx,x,\frac {1}{\log ^2\left (x^2\right )}\right )\\ &=8 \operatorname {Subst}\left (\int e^x \, dx,x,e^{\frac {5}{4 \log ^2\left (x^2\right )}}\right )\\ &=8 e^{e^{\frac {5}{4 \log ^2\left (x^2\right )}}}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.12, size = 16, normalized size = 1.00 \begin {gather*} 8 e^{e^{\frac {5}{4 \log ^2\left (x^2\right )}}} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 1.35, size = 47, normalized size = 2.94 \begin {gather*} e^{\left (\frac {4 \, e^{\left (\frac {5}{4 \, \log \left (x^{2}\right )^{2}}\right )} \log \left (x^{2}\right )^{2} + 12 \, \log \relax (2) \log \left (x^{2}\right )^{2} + 5}{4 \, \log \left (x^{2}\right )^{2}} - \frac {5}{4 \, \log \left (x^{2}\right )^{2}}\right )} \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*} \mathit {undef} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 13, normalized size = 0.81
method | result | size |
risch | \(8 \,{\mathrm e}^{{\mathrm e}^{\frac {5}{4 \ln \left (x^{2}\right )^{2}}}}\) | \(13\) |
derivativedivides | \({\mathrm e}^{{\mathrm e}^{\frac {5}{4 \ln \left (x^{2}\right )^{2}}}+3 \ln \relax (2)}\) | \(16\) |
default | \({\mathrm e}^{{\mathrm e}^{\frac {5}{4 \ln \left (x^{2}\right )^{2}}}+3 \ln \relax (2)}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 10, normalized size = 0.62 \begin {gather*} 8 \, e^{\left (e^{\left (\frac {5}{16 \, \log \relax (x)^{2}}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.60, size = 12, normalized size = 0.75 \begin {gather*} 8\,{\mathrm {e}}^{{\mathrm {e}}^{\frac {5}{4\,{\ln \left (x^2\right )}^2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.41, size = 14, normalized size = 0.88 \begin {gather*} 8 e^{e^{\frac {5}{4 \log {\left (x^{2} \right )}^{2}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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