Integrand size = 9, antiderivative size = 7 \[ \int \frac {1-3 x}{x} \, dx=-390621-3 x+\log (x) \]
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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} \[ \int \frac {1-3 x}{x} \, dx=\log (x)-3 x \]
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Rule 45
Rubi steps \begin{align*} \text {integral}& = \int \left (-3+\frac {1}{x}\right ) \, dx \\ & = -3 x+\log (x) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.86 \[ \int \frac {1-3 x}{x} \, dx=-3 x+\log (x) \]
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Time = 0.01 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.00
method | result | size |
default | \(\ln \left (x \right )-3 x\) | \(7\) |
norman | \(\ln \left (x \right )-3 x\) | \(7\) |
risch | \(\ln \left (x \right )-3 x\) | \(7\) |
parallelrisch | \(\ln \left (x \right )-3 x\) | \(7\) |
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none
Time = 0.22 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.86 \[ \int \frac {1-3 x}{x} \, dx=-3 \, x + \log \left (x\right ) \]
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Time = 0.03 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int \frac {1-3 x}{x} \, dx=- 3 x + \log {\left (x \right )} \]
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none
Time = 0.21 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.86 \[ \int \frac {1-3 x}{x} \, dx=-3 \, x + \log \left (x\right ) \]
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none
Time = 0.27 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.00 \[ \int \frac {1-3 x}{x} \, dx=-3 \, x + \log \left ({\left | x \right |}\right ) \]
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Time = 0.02 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.86 \[ \int \frac {1-3 x}{x} \, dx=\ln \left (x\right )-3\,x \]
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