Optimal. Leaf size=29 \[ 4-2 \left (3+e^2+x\right )+\log \left (\frac {5-\frac {e+2 x}{1+x}}{x}\right ) \]
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Rubi [A] time = 0.06, antiderivative size = 23, normalized size of antiderivative = 0.79, number of steps used = 2, number of rules used = 1, integrand size = 51, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.020, Rules used = {2074} \begin {gather*} -2 x-\log (x)-\log (x+1)+\log (3 x-e+5) \end {gather*}
Antiderivative was successfully verified.
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Rule 2074
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-2-\frac {3}{-5+e-3 x}+\frac {1}{-1-x}-\frac {1}{x}\right ) \, dx\\ &=-2 x-\log (x)-\log (1+x)+\log (5-e+3 x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 23, normalized size = 0.79 \begin {gather*} -2 x-\log (x)-\log (1+x)+\log (5-e+3 x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.71, size = 22, normalized size = 0.76 \begin {gather*} -2 \, x - \log \left (x^{2} + x\right ) + \log \left (3 \, x - e + 5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 27, normalized size = 0.93 \begin {gather*} -2 \, x + \log \left ({\left | 3 \, x - e + 5 \right |}\right ) - \log \left ({\left | x + 1 \right |}\right ) - \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 = 0.06, size = 23, normalized size = 0.79
method | result | size |
norman | \(-2 x -\ln \relax (x )-\ln \left (x +1\right )+\ln \left (-3 x +{\mathrm e}-5\right )\) | \(23\) |
risch | \(-2 x +\ln \left (3 x -{\mathrm e}+5\right )-\ln \left (x^{2}+x \right )\) | \(23\) |
default | \(-2 x -\ln \relax (x )+\ln \left (3 x -{\mathrm e}+5\right )-\ln \left (x +1\right )\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 24, normalized size = 0.83 \begin {gather*} -2 \, x + \log \left (3 \, x - e + 5\right ) - \log \left (x + 1\right ) - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 8.83, size = 20, normalized size = 0.69 \begin {gather*} \ln \left (x-\frac {\mathrm {e}}{3}+\frac {5}{3}\right )-2\,x-\ln \left (x\,\left (x+1\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.48, size = 20, normalized size = 0.69 \begin {gather*} - 2 x - \log {\left (x^{2} + x \right )} + \log {\left (x - \frac {e}{3} + \frac {5}{3} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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