Integrand size = 9, antiderivative size = 7 \[ \int \frac {1-x}{x} \, dx=-1-x+\log (x) \]
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Time = 0.00 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.86, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {45} \[ \int \frac {1-x}{x} \, dx=\log (x)-x \]
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Rule 45
Rubi steps \begin{align*} \text {integral}& = \int \left (-1+\frac {1}{x}\right ) \, dx \\ & = -x+\log (x) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.86 \[ \int \frac {1-x}{x} \, dx=-x+\log (x) \]
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Time = 0.01 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.00
method | result | size |
default | \(\ln \left (x \right )-x\) | \(7\) |
norman | \(\ln \left (x \right )-x\) | \(7\) |
risch | \(\ln \left (x \right )-x\) | \(7\) |
parallelrisch | \(\ln \left (x \right )-x\) | \(7\) |
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none
Time = 0.24 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.86 \[ \int \frac {1-x}{x} \, dx=-x + \log \left (x\right ) \]
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Time = 0.03 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.43 \[ \int \frac {1-x}{x} \, dx=- x + \log {\left (x \right )} \]
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none
Time = 0.18 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.86 \[ \int \frac {1-x}{x} \, dx=-x + \log \left (x\right ) \]
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none
Time = 0.27 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.00 \[ \int \frac {1-x}{x} \, dx=-x + \log \left ({\left | x \right |}\right ) \]
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Time = 0.02 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.86 \[ \int \frac {1-x}{x} \, dx=\ln \left (x\right )-x \]
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