Integrand size = 3, antiderivative size = 4 \[ \int \frac {1}{x} \, dx=\log (-x) \]
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Time = 0.00 (sec) , antiderivative size = 2, normalized size of antiderivative = 0.50, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {29} \[ \int \frac {1}{x} \, dx=\log (x) \]
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Rule 29
Rubi steps \begin{align*} \text {integral}& = \log (x) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 2, normalized size of antiderivative = 0.50 \[ \int \frac {1}{x} \, dx=\log (x) \]
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Time = 0.01 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.75
method | result | size |
default | \(\ln \left (x \right )\) | \(3\) |
norman | \(\ln \left (x \right )\) | \(3\) |
risch | \(\ln \left (x \right )\) | \(3\) |
parallelrisch | \(\ln \left (x \right )\) | \(3\) |
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none
Time = 0.25 (sec) , antiderivative size = 2, normalized size of antiderivative = 0.50 \[ \int \frac {1}{x} \, dx=\log \left (x\right ) \]
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Time = 0.04 (sec) , antiderivative size = 2, normalized size of antiderivative = 0.50 \[ \int \frac {1}{x} \, dx=\log {\left (x \right )} \]
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none
Time = 0.19 (sec) , antiderivative size = 2, normalized size of antiderivative = 0.50 \[ \int \frac {1}{x} \, dx=\log \left (x\right ) \]
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none
Time = 0.26 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.75 \[ \int \frac {1}{x} \, dx=\log \left ({\left | x \right |}\right ) \]
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Time = 0.01 (sec) , antiderivative size = 2, normalized size of antiderivative = 0.50 \[ \int \frac {1}{x} \, dx=\ln \left (x\right ) \]
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