Optimal. Leaf size=17 \[ e^x (1+3 \log (4+x) \log (2 \log (5))) \]
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Rubi [A] time = 0.34, antiderivative size = 16, normalized size of antiderivative = 0.94, number of steps used = 9, number of rules used = 6, integrand size = 39, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {6741, 6742, 2194, 2554, 2178, 2199} \begin {gather*} e^x+3 e^x \log (\log (25)) \log (x+4) \end {gather*}
Antiderivative was successfully verified.
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Rule 2178
Rule 2194
Rule 2199
Rule 2554
Rule 6741
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^x \left (x+4 \left (1+\frac {3}{4} \log (\log (25))\right )+12 \log (4+x) \log (\log (25))+3 x \log (4+x) \log (\log (25))\right )}{4+x} \, dx\\ &=\int \left (3 e^x \log (4+x) \log (\log (25))+\frac {e^x (4+x+3 \log (\log (25)))}{4+x}\right ) \, dx\\ &=(3 \log (\log (25))) \int e^x \log (4+x) \, dx+\int \frac {e^x (4+x+3 \log (\log (25)))}{4+x} \, dx\\ &=3 e^x \log (4+x) \log (\log (25))-(3 \log (\log (25))) \int \frac {e^x}{4+x} \, dx+\int \left (e^x+\frac {3 e^x \log (\log (25))}{4+x}\right ) \, dx\\ &=-\frac {3 \text {Ei}(4+x) \log (\log (25))}{e^4}+3 e^x \log (4+x) \log (\log (25))+(3 \log (\log (25))) \int \frac {e^x}{4+x} \, dx+\int e^x \, dx\\ &=e^x+3 e^x \log (4+x) \log (\log (25))\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 15, normalized size = 0.88 \begin {gather*} e^x (1+3 \log (4+x) \log (\log (25))) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 16, normalized size = 0.94 \begin {gather*} 3 \, e^{x} \log \left (x + 4\right ) \log \left (2 \, \log \relax (5)\right ) + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.27, size = 16, normalized size = 0.94 \begin {gather*} 3 \, e^{x} \log \left (x + 4\right ) \log \left (2 \, \log \relax (5)\right ) + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 17, normalized size = 1.00
method | result | size |
default | \(3 \ln \left (2 \ln \relax (5)\right ) {\mathrm e}^{x} \ln \left (4+x \right )+{\mathrm e}^{x}\) | \(17\) |
risch | \(3 \left (\ln \relax (2)+\ln \left (\ln \relax (5)\right )\right ) {\mathrm e}^{x} \ln \left (4+x \right )+{\mathrm e}^{x}\) | \(18\) |
norman | \(\left (3 \ln \relax (2)+3 \ln \left (\ln \relax (5)\right )\right ) {\mathrm e}^{x} \ln \left (4+x \right )+{\mathrm e}^{x}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} -3 \, e^{\left (-4\right )} E_{1}\left (-x - 4\right ) \log \left (2 \, \log \relax (5)\right ) - 4 \, e^{\left (-4\right )} E_{1}\left (-x - 4\right ) + \frac {3 \, {\left (x {\left (\log \relax (2) + \log \left (\log \relax (5)\right )\right )} + 4 \, \log \relax (2) + 4 \, \log \left (\log \relax (5)\right )\right )} e^{x} \log \left (x + 4\right ) + x e^{x}}{x + 4} - \int \frac {{\left (3 \, x {\left (\log \relax (2) + \log \left (\log \relax (5)\right )\right )} + 12 \, \log \relax (2) + 12 \, \log \left (\log \relax (5)\right ) + 4\right )} e^{x}}{x^{2} + 8 \, x + 16}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.38, size = 14, normalized size = 0.82 \begin {gather*} {\mathrm {e}}^x\,\left (3\,\ln \left (x+4\right )\,\ln \left (\ln \left (25\right )\right )+1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.45, size = 26, normalized size = 1.53 \begin {gather*} \left (3 \log {\left (x + 4 \right )} \log {\left (\log {\relax (5 )} \right )} + 3 \log {\relax (2 )} \log {\left (x + 4 \right )} + 1\right ) e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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