Optimal. Leaf size=27 \[ \left (5-e^2\right ) \left (-4+\frac {-4+(2+2 x)^2}{x}+\log (3 x)\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 21, normalized size of antiderivative = 0.78, number of steps
used = 3, number of rules used = 2, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {192, 45}
\begin {gather*} 4 \left (5-e^2\right ) x+\left (5-e^2\right ) \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rule 192
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {5-e^2+4 \left (5-e^2\right ) x}{x} \, dx\\ &=\int \left (4 \left (5-e^2\right )+\frac {5-e^2}{x}\right ) \, dx\\ &=4 \left (5-e^2\right ) x+\left (5-e^2\right ) \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 13, normalized size = 0.48 \begin {gather*} -\left (\left (-5+e^2\right ) (4 x+\log (x))\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.20, size = 14, normalized size = 0.52
method | result | size |
default | \(\left ({\mathrm e}^{2}-5\right ) \left (-\ln \left (x \right )-4 x \right )\) | \(14\) |
norman | \(\left (-4 \,{\mathrm e}^{2}+20\right ) x +\left (5-{\mathrm e}^{2}\right ) \ln \left (x \right )\) | \(19\) |
risch | \(-4 \,{\mathrm e}^{2} x +20 x -{\mathrm e}^{2} \ln \left (x \right )+5 \ln \left (x \right )\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 16, normalized size = 0.59 \begin {gather*} -4 \, x {\left (e^{2} - 5\right )} - {\left (e^{2} - 5\right )} \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.46, size = 17, normalized size = 0.63 \begin {gather*} -4 \, x e^{2} - {\left (e^{2} - 5\right )} \log \left (x\right ) + 20 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 15, normalized size = 0.56 \begin {gather*} x \left (20 - 4 e^{2}\right ) + \left (5 - e^{2}\right ) \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.38, size = 18, normalized size = 0.67 \begin {gather*} -4 \, x e^{2} - {\left (e^{2} - 5\right )} \log \left ({\left | x \right |}\right ) + 20 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.06, size = 12, normalized size = 0.44 \begin {gather*} -\left (4\,x+\ln \left (x\right )\right )\,\left ({\mathrm {e}}^2-5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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