Optimal. Leaf size=19 \[ e^{4+x}+\frac {4}{5} (2+x-\log (4 x)) \]
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Rubi [A] time = 0.01, antiderivative size = 17, normalized size of antiderivative = 0.89, number of steps used = 6, number of rules used = 4, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {12, 14, 2194, 43} \begin {gather*} \frac {4 x}{5}+e^{x+4}-\frac {4 \log (x)}{5} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 43
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \frac {-4+4 x+5 e^{4+x} x}{x} \, dx\\ &=\frac {1}{5} \int \left (5 e^{4+x}+\frac {4 (-1+x)}{x}\right ) \, dx\\ &=\frac {4}{5} \int \frac {-1+x}{x} \, dx+\int e^{4+x} \, dx\\ &=e^{4+x}+\frac {4}{5} \int \left (1-\frac {1}{x}\right ) \, dx\\ &=e^{4+x}+\frac {4 x}{5}-\frac {4 \log (x)}{5}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 17, normalized size = 0.89 \begin {gather*} e^{4+x}+\frac {4 x}{5}-\frac {4 \log (x)}{5} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.70, size = 12, normalized size = 0.63 \begin {gather*} \frac {4}{5} \, x + e^{\left (x + 4\right )} - \frac {4}{5} \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 12, normalized size = 0.63 \begin {gather*} \frac {4}{5} \, x + e^{\left (x + 4\right )} - \frac {4}{5} \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 13, normalized size = 0.68
method | result | size |
norman | \(\frac {4 x}{5}+{\mathrm e}^{4+x}-\frac {4 \ln \relax (x )}{5}\) | \(13\) |
risch | \(\frac {4 x}{5}+{\mathrm e}^{4+x}-\frac {4 \ln \relax (x )}{5}\) | \(13\) |
derivativedivides | \(-\frac {4 \ln \relax (x )}{5}+\frac {16}{5}+\frac {4 x}{5}+{\mathrm e}^{4+x}\) | \(14\) |
default | \(-\frac {4 \ln \relax (x )}{5}+\frac {16}{5}+\frac {4 x}{5}+{\mathrm e}^{4+x}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 12, normalized size = 0.63 \begin {gather*} \frac {4}{5} \, x + e^{\left (x + 4\right )} - \frac {4}{5} \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.50, size = 12, normalized size = 0.63 \begin {gather*} \frac {4\,x}{5}+{\mathrm {e}}^{x+4}-\frac {4\,\ln \relax (x)}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 15, normalized size = 0.79 \begin {gather*} \frac {4 x}{5} + e^{x + 4} - \frac {4 \log {\relax (x )}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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