Integrand size = 11, antiderivative size = 17 \[ \int \frac {-1-x}{-2+x} \, dx=-4-x+3 (-2-\log (2-x)) \]
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Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.71, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {45} \[ \int \frac {-1-x}{-2+x} \, dx=-x-3 \log (2-x) \]
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Rule 45
Rubi steps \begin{align*} \text {integral}& = \int \left (-1-\frac {3}{-2+x}\right ) \, dx \\ & = -x-3 \log (2-x) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.71 \[ \int \frac {-1-x}{-2+x} \, dx=-x-3 \log (2-x) \]
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Time = 0.42 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.65
method | result | size |
default | \(-x -3 \ln \left (-2+x \right )\) | \(11\) |
norman | \(-x -3 \ln \left (-2+x \right )\) | \(11\) |
risch | \(-x -3 \ln \left (-2+x \right )\) | \(11\) |
parallelrisch | \(-x -3 \ln \left (-2+x \right )\) | \(11\) |
meijerg | \(-3 \ln \left (1-\frac {x}{2}\right )-x\) | \(13\) |
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none
Time = 0.25 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.59 \[ \int \frac {-1-x}{-2+x} \, dx=-x - 3 \, \log \left (x - 2\right ) \]
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Time = 0.03 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.47 \[ \int \frac {-1-x}{-2+x} \, dx=- x - 3 \log {\left (x - 2 \right )} \]
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none
Time = 0.20 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.59 \[ \int \frac {-1-x}{-2+x} \, dx=-x - 3 \, \log \left (x - 2\right ) \]
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none
Time = 0.26 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.65 \[ \int \frac {-1-x}{-2+x} \, dx=-x - 3 \, \log \left ({\left | x - 2 \right |}\right ) \]
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Time = 0.03 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.59 \[ \int \frac {-1-x}{-2+x} \, dx=-x-3\,\ln \left (x-2\right ) \]
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