Integrand size = 9, antiderivative size = 15 \[ \int \frac {1-4 x}{x} \, dx=x \left (-3+\frac {-5-x+\log (x)}{x}\right ) \]
[Out]
Time = 0.00 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.40, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {45} \[ \int \frac {1-4 x}{x} \, dx=\log (x)-4 x \]
[In]
[Out]
Rule 45
Rubi steps \begin{align*} \text {integral}& = \int \left (-4+\frac {1}{x}\right ) \, dx \\ & = -4 x+\log (x) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.40 \[ \int \frac {1-4 x}{x} \, dx=-4 x+\log (x) \]
[In]
[Out]
Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.47
method | result | size |
default | \(-4 x +\ln \left (x \right )\) | \(7\) |
norman | \(-4 x +\ln \left (x \right )\) | \(7\) |
risch | \(-4 x +\ln \left (x \right )\) | \(7\) |
parallelrisch | \(-4 x +\ln \left (x \right )\) | \(7\) |
[In]
[Out]
none
Time = 0.25 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.40 \[ \int \frac {1-4 x}{x} \, dx=-4 \, x + \log \left (x\right ) \]
[In]
[Out]
Time = 0.03 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.33 \[ \int \frac {1-4 x}{x} \, dx=- 4 x + \log {\left (x \right )} \]
[In]
[Out]
none
Time = 0.18 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.40 \[ \int \frac {1-4 x}{x} \, dx=-4 \, x + \log \left (x\right ) \]
[In]
[Out]
none
Time = 0.27 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.47 \[ \int \frac {1-4 x}{x} \, dx=-4 \, x + \log \left ({\left | x \right |}\right ) \]
[In]
[Out]
Time = 0.02 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.40 \[ \int \frac {1-4 x}{x} \, dx=\ln \left (x\right )-4\,x \]
[In]
[Out]