Optimal. Leaf size=21 \[ e^x+\frac {512}{25} \left (x^2+\log \left (\frac {4 x}{3}+\log (2)\right )\right ) \]
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Rubi [A] time = 0.13, antiderivative size = 22, normalized size of antiderivative = 1.05, number of steps used = 5, number of rules used = 3, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.086, Rules used = {6742, 2194, 698} \begin {gather*} \frac {512 x^2}{25}+e^x+\frac {512}{25} \log (4 x+\log (8)) \end {gather*}
Antiderivative was successfully verified.
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Rule 698
Rule 2194
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (e^x+\frac {1024 \left (2+4 x^2+x \log (8)\right )}{25 (4 x+\log (8))}\right ) \, dx\\ &=\frac {1024}{25} \int \frac {2+4 x^2+x \log (8)}{4 x+\log (8)} \, dx+\int e^x \, dx\\ &=e^x+\frac {1024}{25} \int \left (x+\frac {2}{4 x+\log (8)}\right ) \, dx\\ &=e^x+\frac {512 x^2}{25}+\frac {512}{25} \log (4 x+\log (8))\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 30, normalized size = 1.43 \begin {gather*} \frac {1}{25} \left (25 e^x+512 x^2-32 \log ^2(8)+512 \log (4 x+\log (8))\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.11, size = 19, normalized size = 0.90 \begin {gather*} \frac {512}{25} \, x^{2} + e^{x} + \frac {512}{25} \, \log \left (4 \, x + 3 \, \log \relax (2)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.28, size = 19, normalized size = 0.90 \begin {gather*} \frac {512}{25} \, x^{2} + e^{x} + \frac {512}{25} \, \log \left (4 \, x + 3 \, \log \relax (2)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.44, size = 20, normalized size = 0.95
method | result | size |
default | \(\frac {512 \ln \left (3 \ln \relax (2)+4 x \right )}{25}+\frac {512 x^{2}}{25}+{\mathrm e}^{x}\) | \(20\) |
norman | \(\frac {512 x^{2}}{25}+{\mathrm e}^{x}+\frac {512 \ln \left (75 \ln \relax (2)+100 x \right )}{25}\) | \(20\) |
risch | \(\frac {512 \ln \left (3 \ln \relax (2)+4 x \right )}{25}+\frac {512 x^{2}}{25}+{\mathrm e}^{x}\) | \(20\) |
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*} \frac {576}{25} \, \log \relax (2)^{2} \log \left (4 \, x + 3 \, \log \relax (2)\right ) - \frac {3}{8} \cdot 2^{\frac {1}{4}} E_{1}\left (-x - \frac {3}{4} \, \log \relax (2)\right ) \log \relax (2) + \frac {512}{25} \, x^{2} - \frac {192}{25} \, {\left (3 \, \log \relax (2) \log \left (4 \, x + 3 \, \log \relax (2)\right ) - 4 \, x\right )} \log \relax (2) - \frac {768}{25} \, x \log \relax (2) - 12 \, \int \frac {e^{x}}{16 \, x^{2} + 24 \, x \log \relax (2) + 9 \, \log \relax (2)^{2}}\,{d x} \log \relax (2) + \frac {4 \, x e^{x}}{4 \, x + 3 \, \log \relax (2)} + \frac {512}{25} \, \log \left (4 \, x + 3 \, \log \relax (2)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.09, size = 17, normalized size = 0.81 \begin {gather*} \frac {512\,\ln \left (4\,x+\ln \relax (8)\right )}{25}+{\mathrm {e}}^x+\frac {512\,x^2}{25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 22, normalized size = 1.05 \begin {gather*} \frac {512 x^{2}}{25} + e^{x} + \frac {512 \log {\left (4 x + 3 \log {\relax (2 )} \right )}}{25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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