Optimal. Leaf size=14 \[ -8+e^4-x+\log (2)+\log (-5+x) \]
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Rubi [A]
time = 0.00, antiderivative size = 10, normalized size of antiderivative = 0.71, number of steps
used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {45}
\begin {gather*} \log (5-x)-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 {1}{-5+x}\right ) \, dx\\ &=-x+\log (5-x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 8, normalized size = 0.57 \begin {gather*} -x+\log (-5+x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 9, normalized size = 0.64
method | result | size |
default | \(-x +\ln \left (x -5\right )\) | \(9\) |
norman | \(-x +\ln \left (x -5\right )\) | \(9\) |
risch | \(-x +\ln \left (x -5\right )\) | \(9\) |
meijerg | \(\ln \left (1-\frac {x}{5}\right )-x\) | \(11\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 8, normalized size = 0.57 \begin {gather*} -x + \log \left (x - 5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.30, size = 8, normalized size = 0.57 \begin {gather*} -x + \log \left (x - 5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 5, normalized size = 0.36 \begin {gather*} - x + \log {\left (x - 5 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 9, normalized size = 0.64 \begin {gather*} -x + \log \left ({\left | x - 5 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 8, normalized size = 0.57 \begin {gather*} \ln \left (x-5\right )-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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