Optimal. Leaf size=19 \[ x-\log \left (\frac {5-\log (4)}{4-5 x}\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 8, normalized size of antiderivative = 0.42, number of steps
used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {45}
\begin {gather*} x+\log (4-5 x) \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1+\frac {5}{-4+5 x}\right ) \, dx\\ &=x+\log (4-5 x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 8, normalized size = 0.42 \begin {gather*} x+\log (-4+5 x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 6.78, size = 9, normalized size = 0.47
method | result | size |
default | \(x +\ln \left (5 x -4\right )\) | \(9\) |
norman | \(x +\ln \left (5 x -4\right )\) | \(9\) |
meijerg | \(\ln \left (1-\frac {5 x}{4}\right )+x\) | \(9\) |
risch | \(x +\ln \left (5 x -4\right )\) | \(9\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 8, normalized size = 0.42 \begin {gather*} x + \log \left (5 \, x - 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 8, normalized size = 0.42 \begin {gather*} x + \log \left (5 \, x - 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 7, normalized size = 0.37 \begin {gather*} x + \log {\left (5 x - 4 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 9, normalized size = 0.47 \begin {gather*} x + \log \left ({\left | 5 \, x - 4 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.06, size = 6, normalized size = 0.32 \begin {gather*} x+\ln \left (x-\frac {4}{5}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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