Optimal. Leaf size=25 \[ 1+e^{\frac {-\log ^2(2)+\frac {x}{9 \log ^4(x)}}{x}}+x \]
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Rubi [A] time = 0.96, antiderivative size = 22, normalized size of antiderivative = 0.88, number of steps used = 4, number of rules used = 3, integrand size = 61, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.049, Rules used = {12, 6742, 6706} \begin {gather*} x+e^{\frac {1}{9 \log ^4(x)}-\frac {\log ^2(2)}{x}} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6706
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{9} \int \frac {9 x^2 \log ^5(x)+e^{\frac {x-9 \log ^2(2) \log ^4(x)}{9 x \log ^4(x)}} \left (-4 x+9 \log ^2(2) \log ^5(x)\right )}{x^2 \log ^5(x)} \, dx\\ &=\frac {1}{9} \int \left (9-\frac {e^{-\frac {\log ^2(2)}{x}+\frac {1}{9 \log ^4(x)}} \left (4 x-9 \log ^2(2) \log ^5(x)\right )}{x^2 \log ^5(x)}\right ) \, dx\\ &=x-\frac {1}{9} \int \frac {e^{-\frac {\log ^2(2)}{x}+\frac {1}{9 \log ^4(x)}} \left (4 x-9 \log ^2(2) \log ^5(x)\right )}{x^2 \log ^5(x)} \, dx\\ &=e^{-\frac {\log ^2(2)}{x}+\frac {1}{9 \log ^4(x)}}+x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.17, size = 22, normalized size = 0.88 \begin {gather*} e^{-\frac {\log ^2(2)}{x}+\frac {1}{9 \log ^4(x)}}+x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.46, size = 26, normalized size = 1.04 \begin {gather*} x + e^{\left (-\frac {9 \, \log \relax (2)^{2} \log \relax (x)^{4} - x}{9 \, x \log \relax (x)^{4}}\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 = 0.09, size = 27, normalized size = 1.08
method | result | size |
risch | \(x +{\mathrm e}^{-\frac {9 \ln \relax (2)^{2} \ln \relax (x )^{4}-x}{9 x \ln \relax (x )^{4}}}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.61, size = 19, normalized size = 0.76 \begin {gather*} x + e^{\left (-\frac {\log \relax (2)^{2}}{x} + \frac {1}{9 \, \log \relax (x)^{4}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.11, size = 20, normalized size = 0.80 \begin {gather*} x+{\mathrm {e}}^{\frac {1}{9\,{\ln \relax (x)}^4}}\,{\mathrm {e}}^{-\frac {{\ln \relax (2)}^2}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.36, size = 22, normalized size = 0.88 \begin {gather*} x + e^{\frac {\frac {x}{9} - \log {\relax (2 )}^{2} \log {\relax (x )}^{4}}{x \log {\relax (x )}^{4}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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