Integrand size = 7, antiderivative size = 10 \[ \int \frac {x}{-5+x} \, dx=x+5 \log (5-x) \]
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Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {45} \[ \int \frac {x}{-5+x} \, dx=x+5 \log (5-x) \]
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Rule 45
Rubi steps \begin{align*} \text {integral}& = \int \left (1+\frac {5}{-5+x}\right ) \, dx \\ & = x+5 \log (5-x) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \frac {x}{-5+x} \, dx=x+5 \log (-5+x) \]
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Time = 0.14 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.90
method | result | size |
default | \(x +5 \ln \left (x -5\right )\) | \(9\) |
norman | \(x +5 \ln \left (x -5\right )\) | \(9\) |
risch | \(x +5 \ln \left (x -5\right )\) | \(9\) |
parallelrisch | \(x +5 \ln \left (x -5\right )\) | \(9\) |
meijerg | \(x +5 \ln \left (1-\frac {x}{5}\right )\) | \(11\) |
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none
Time = 0.23 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \frac {x}{-5+x} \, dx=x + 5 \, \log \left (x - 5\right ) \]
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Time = 0.03 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.70 \[ \int \frac {x}{-5+x} \, dx=x + 5 \log {\left (x - 5 \right )} \]
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none
Time = 0.20 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \frac {x}{-5+x} \, dx=x + 5 \, \log \left (x - 5\right ) \]
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none
Time = 0.27 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.90 \[ \int \frac {x}{-5+x} \, dx=x + 5 \, \log \left ({\left | x - 5 \right |}\right ) \]
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Time = 0.03 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \frac {x}{-5+x} \, dx=x+5\,\ln \left (x-5\right ) \]
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