Integrand size = 9, antiderivative size = 12 \[ \int -\frac {4}{x \log (2)} \, dx=\frac {4 (5-\log (x))}{\log (2)} \]
[Out]
Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {12, 29} \[ \int -\frac {4}{x \log (2)} \, dx=-\frac {4 \log (x)}{\log (2)} \]
[In]
[Out]
Rule 12
Rule 29
Rubi steps \begin{align*} \text {integral}& = -\frac {4 \int \frac {1}{x} \, dx}{\log (2)} \\ & = -\frac {4 \log (x)}{\log (2)} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int -\frac {4}{x \log (2)} \, dx=-\frac {4 \log (x)}{\log (2)} \]
[In]
[Out]
Time = 0.04 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.75
method | result | size |
default | \(-\frac {4 \ln \left (x \right )}{\ln \left (2\right )}\) | \(9\) |
norman | \(-\frac {4 \ln \left (x \right )}{\ln \left (2\right )}\) | \(9\) |
risch | \(-\frac {4 \ln \left (x \right )}{\ln \left (2\right )}\) | \(9\) |
parallelrisch | \(-\frac {4 \ln \left (x \right )}{\ln \left (2\right )}\) | \(9\) |
[In]
[Out]
none
Time = 0.24 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int -\frac {4}{x \log (2)} \, dx=-\frac {4 \, \log \left (x\right )}{\log \left (2\right )} \]
[In]
[Out]
Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int -\frac {4}{x \log (2)} \, dx=- \frac {4 \log {\left (x \right )}}{\log {\left (2 \right )}} \]
[In]
[Out]
none
Time = 0.19 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int -\frac {4}{x \log (2)} \, dx=-\frac {4 \, \log \left (x\right )}{\log \left (2\right )} \]
[In]
[Out]
none
Time = 0.26 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.75 \[ \int -\frac {4}{x \log (2)} \, dx=-\frac {4 \, \log \left ({\left | x \right |}\right )}{\log \left (2\right )} \]
[In]
[Out]
Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int -\frac {4}{x \log (2)} \, dx=-\frac {4\,\ln \left (x\right )}{\ln \left (2\right )} \]
[In]
[Out]