Optimal. Leaf size=10 \[ x+5 \log (5-x) \]
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Rubi [A]
time = 0.00, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {45}
\begin {gather*} x+5 \log (5-x) \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int \frac {x}{-5+x} \, dx &=\int \left (1+\frac {5}{-5+x}\right ) \, dx\\ &=x+5 \log (5-x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 8, normalized size = 0.80 \begin {gather*} x+5 \log (-5+x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.05, size = 9, normalized size = 0.90
method | result | size |
default | \(x +5 \ln \left (x -5\right )\) | \(9\) |
norman | \(x +5 \ln \left (x -5\right )\) | \(9\) |
risch | \(x +5 \ln \left (x -5\right )\) | \(9\) |
meijerg | \(x +5 \ln \left (1-\frac {x}{5}\right )\) | \(11\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 1.87, size = 8, normalized size = 0.80 \begin {gather*} x + 5 \, \log \left (x - 5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.51, size = 8, normalized size = 0.80 \begin {gather*} x + 5 \, \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 = 7, normalized size = 0.70 \begin {gather*} x + 5 \log {\left (x - 5 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.47, size = 9, normalized size = 0.90 \begin {gather*} x + 5 \, \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 = 0.80 \begin {gather*} x+5\,\ln \left (x-5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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