Integrand size = 9, antiderivative size = 11 \[ \int \frac {4-4 x}{x} \, dx=-1+4 (1-x+\log (x)) \]
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Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {45} \[ \int \frac {4-4 x}{x} \, dx=4 \log (x)-4 x \]
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Rule 45
Rubi steps \begin{align*} \text {integral}& = \int \left (-4+\frac {4}{x}\right ) \, dx \\ & = -4 x+4 \log (x) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int \frac {4-4 x}{x} \, dx=-4 x+4 \log (x) \]
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Time = 0.02 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82
method | result | size |
default | \(4 \ln \left (x \right )-4 x\) | \(9\) |
norman | \(4 \ln \left (x \right )-4 x\) | \(9\) |
risch | \(4 \ln \left (x \right )-4 x\) | \(9\) |
parallelrisch | \(4 \ln \left (x \right )-4 x\) | \(9\) |
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none
Time = 0.25 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int \frac {4-4 x}{x} \, dx=-4 \, x + 4 \, \log \left (x\right ) \]
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Time = 0.03 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.64 \[ \int \frac {4-4 x}{x} \, dx=- 4 x + 4 \log {\left (x \right )} \]
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none
Time = 0.17 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int \frac {4-4 x}{x} \, dx=-4 \, x + 4 \, \log \left (x\right ) \]
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none
Time = 0.27 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82 \[ \int \frac {4-4 x}{x} \, dx=-4 \, x + 4 \, \log \left ({\left | x \right |}\right ) \]
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Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int \frac {4-4 x}{x} \, dx=4\,\ln \left (x\right )-4\,x \]
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