Integrand size = 15, antiderivative size = 11 \[ \int \frac {10-5 \log (\log (6))}{x \log ^2(x)} \, dx=\frac {5 (-2+\log (\log (6)))}{\log (x)} \]
[Out]
Time = 0.01 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.18, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {12, 2339, 30} \[ \int \frac {10-5 \log (\log (6))}{x \log ^2(x)} \, dx=-\frac {5 (2-\log (\log (6)))}{\log (x)} \]
[In]
[Out]
Rule 12
Rule 30
Rule 2339
Rubi steps \begin{align*} \text {integral}& = (5 (2-\log (\log (6)))) \int \frac {1}{x \log ^2(x)} \, dx \\ & = (5 (2-\log (\log (6)))) \text {Subst}\left (\int \frac {1}{x^2} \, dx,x,\log (x)\right ) \\ & = -\frac {5 (2-\log (\log (6)))}{\log (x)} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.45 \[ \int \frac {10-5 \log (\log (6))}{x \log ^2(x)} \, dx=-\frac {10}{\log (x)}+\frac {5 \log (\log (6))}{\log (x)} \]
[In]
[Out]
Time = 0.14 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.18
method | result | size |
norman | \(\frac {5 \ln \left (\ln \left (6\right )\right )-10}{\ln \left (x \right )}\) | \(13\) |
derivativedivides | \(-\frac {-5 \ln \left (\ln \left (6\right )\right )+10}{\ln \left (x \right )}\) | \(14\) |
default | \(-\frac {-5 \ln \left (\ln \left (6\right )\right )+10}{\ln \left (x \right )}\) | \(14\) |
parallelrisch | \(-\frac {-5 \ln \left (\ln \left (6\right )\right )+10}{\ln \left (x \right )}\) | \(14\) |
risch | \(\frac {5 \ln \left (\ln \left (2\right )+\ln \left (3\right )\right )}{\ln \left (x \right )}-\frac {10}{\ln \left (x \right )}\) | \(20\) |
[In]
[Out]
none
Time = 0.24 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int \frac {10-5 \log (\log (6))}{x \log ^2(x)} \, dx=\frac {5 \, {\left (\log \left (\log \left (6\right )\right ) - 2\right )}}{\log \left (x\right )} \]
[In]
[Out]
Time = 0.03 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.91 \[ \int \frac {10-5 \log (\log (6))}{x \log ^2(x)} \, dx=\frac {-10 + 5 \log {\left (\log {\left (6 \right )} \right )}}{\log {\left (x \right )}} \]
[In]
[Out]
none
Time = 0.19 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int \frac {10-5 \log (\log (6))}{x \log ^2(x)} \, dx=\frac {5 \, {\left (\log \left (\log \left (6\right )\right ) - 2\right )}}{\log \left (x\right )} \]
[In]
[Out]
none
Time = 0.28 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int \frac {10-5 \log (\log (6))}{x \log ^2(x)} \, dx=\frac {5 \, {\left (\log \left (\log \left (6\right )\right ) - 2\right )}}{\log \left (x\right )} \]
[In]
[Out]
Time = 0.05 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.09 \[ \int \frac {10-5 \log (\log (6))}{x \log ^2(x)} \, dx=\frac {5\,\ln \left (\ln \left (6\right )\right )-10}{\ln \left (x\right )} \]
[In]
[Out]