Optimal. Leaf size=17 \[ \frac {17}{5}+x+\frac {12 x (25+x+\log (\log (x)))}{e^5} \]
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Rubi [A] time = 0.13, antiderivative size = 28, normalized size of antiderivative = 1.65, number of steps used = 9, number of rules used = 5, integrand size = 56, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.089, Rules used = {6688, 12, 6742, 2298, 2520} \begin {gather*} \frac {12 x^2}{e^5}+\frac {\left (300+e^5\right ) x}{e^5}+\frac {12 x \log (\log (x))}{e^5} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2298
Rule 2520
Rule 6688
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {12+\log (x) \left (300+e^5+24 x+12 \log (\log (x))\right )}{e^5 \log (x)} \, dx\\ &=\frac {\int \frac {12+\log (x) \left (300+e^5+24 x+12 \log (\log (x))\right )}{\log (x)} \, dx}{e^5}\\ &=\frac {\int \left (\frac {12+300 \left (1+\frac {e^5}{300}\right ) \log (x)+24 x \log (x)}{\log (x)}+12 \log (\log (x))\right ) \, dx}{e^5}\\ &=\frac {\int \frac {12+300 \left (1+\frac {e^5}{300}\right ) \log (x)+24 x \log (x)}{\log (x)} \, dx}{e^5}+\frac {12 \int \log (\log (x)) \, dx}{e^5}\\ &=\frac {12 x \log (\log (x))}{e^5}+\frac {\int \left (300+e^5+24 x+\frac {12}{\log (x)}\right ) \, dx}{e^5}-\frac {12 \int \frac {1}{\log (x)} \, dx}{e^5}\\ &=\frac {\left (300+e^5\right ) x}{e^5}+\frac {12 x^2}{e^5}+\frac {12 x \log (\log (x))}{e^5}-\frac {12 \text {li}(x)}{e^5}+\frac {12 \int \frac {1}{\log (x)} \, dx}{e^5}\\ &=\frac {\left (300+e^5\right ) x}{e^5}+\frac {12 x^2}{e^5}+\frac {12 x \log (\log (x))}{e^5}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.05, size = 19, normalized size = 1.12 \begin {gather*} \frac {x \left (e^5+12 (25+x)+12 \log (\log (x))\right )}{e^5} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.72, size = 22, normalized size = 1.29 \begin {gather*} {\left (12 \, x^{2} + x e^{5} + 12 \, x \log \left (\log \relax (x)\right ) + 300 \, x\right )} e^{\left (-5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.49, size = 22, normalized size = 1.29 \begin {gather*} 12 \, x^{2} e^{\left (-5\right )} + 12 \, x e^{\left (-5\right )} \log \left (\log \relax (x)\right ) + 300 \, x e^{\left (-5\right )} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 23, normalized size = 1.35
method | result | size |
default | \(x +12 \ln \left (\ln \relax (x )\right ) {\mathrm e}^{-5} x +12 \,{\mathrm e}^{-5} x^{2}+300 x \,{\mathrm e}^{-5}\) | \(23\) |
risch | \(x +12 \ln \left (\ln \relax (x )\right ) {\mathrm e}^{-5} x +12 \,{\mathrm e}^{-5} x^{2}+300 x \,{\mathrm e}^{-5}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.93, size = 21, normalized size = 1.24 \begin {gather*} {\left (12 \, x^{2} + x {\left (e^{5} + 300\right )} + 12 \, x \log \left (\log \relax (x)\right )\right )} e^{\left (-5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.58, size = 16, normalized size = 0.94 \begin {gather*} x\,{\mathrm {e}}^{-5}\,\left (12\,x+12\,\ln \left (\ln \relax (x)\right )+{\mathrm {e}}^5+300\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.33, size = 29, normalized size = 1.71 \begin {gather*} \frac {12 x^{2}}{e^{5}} + \frac {12 x \log {\left (\log {\relax (x )} \right )}}{e^{5}} + \frac {x \left (e^{5} + 300\right )}{e^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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