Optimal. Leaf size=21 \[ 1+5 \left (-x+\log \left (x \left (e^2+x\right )\right )\right )+\log (6+\log (4)) \]
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Rubi [A] time = 0.04, antiderivative size = 16, normalized size of antiderivative = 0.76, number of steps used = 3, number of rules used = 2, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {1593, 1820} \begin {gather*} -5 x+5 \log (x)+5 \log \left (x+e^2\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 1593
Rule 1820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^2 (5-5 x)+10 x-5 x^2}{x \left (e^2+x\right )} \, dx\\ &=\int \left (-5+\frac {5}{x}+\frac {5}{e^2+x}\right ) \, dx\\ &=-5 x+5 \log (x)+5 \log \left (e^2+x\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 16, normalized size = 0.76 \begin {gather*} -5 \left (x-\log (x)-\log \left (e^2+x\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.75, size = 15, normalized size = 0.71 \begin {gather*} -5 \, x + 5 \, \log \left (x^{2} + x e^{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 17, normalized size = 0.81 \begin {gather*} -5 \, x + 5 \, \log \left ({\left | x + e^{2} \right |}\right ) + 5 \, \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.47, size = 16, normalized size = 0.76
method | result | size |
default | \(-5 x +5 \ln \relax (x )+5 \ln \left (x +{\mathrm e}^{2}\right )\) | \(16\) |
norman | \(-5 x +5 \ln \relax (x )+5 \ln \left (x +{\mathrm e}^{2}\right )\) | \(16\) |
risch | \(-5 x +5 \ln \left ({\mathrm e}^{2} x +x^{2}\right )\) | \(16\) |
meijerg | \(5 \ln \relax (x )-10-5 \ln \left (1+x \,{\mathrm e}^{-2}\right )+\left (-5 \,{\mathrm e}^{2}+10\right ) \ln \left (1+x \,{\mathrm e}^{-2}\right )-5 \,{\mathrm e}^{2} \left (x \,{\mathrm e}^{-2}-\ln \left (1+x \,{\mathrm e}^{-2}\right )\right )\) | \(48\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 15, normalized size = 0.71 \begin {gather*} -5 \, x + 5 \, \log \left (x + e^{2}\right ) + 5 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.10, size = 13, normalized size = 0.62 \begin {gather*} 5\,\ln \left (x\,\left (x+{\mathrm {e}}^2\right )\right )-5\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 14, normalized size = 0.67 \begin {gather*} - 5 x + 5 \log {\left (x^{2} + x e^{2} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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