Integrand size = 16, antiderivative size = 12 \[ \int \frac {7-\log (x)}{x (3+\log (x))} \, dx=-\log (x)+10 \log (3+\log (x)) \]
[Out]
Time = 0.02 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {2412, 45} \[ \int \frac {7-\log (x)}{x (3+\log (x))} \, dx=10 \log (\log (x)+3)-\log (x) \]
[In]
[Out]
Rule 45
Rule 2412
Rubi steps \begin{align*} \text {integral}& = \text {Subst}\left (\int \frac {7-x}{3+x} \, dx,x,\log (x)\right ) \\ & = \text {Subst}\left (\int \left (-1+\frac {10}{3+x}\right ) \, dx,x,\log (x)\right ) \\ & = -\log (x)+10 \log (3+\log (x)) \\ \end{align*}
Time = 0.04 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {7-\log (x)}{x (3+\log (x))} \, dx=-\log (x)+10 \log (3+\log (x)) \]
[In]
[Out]
Time = 0.20 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.08
method | result | size |
derivativedivides | \(-\ln \left (x \right )+10 \ln \left (3+\ln \left (x \right )\right )\) | \(13\) |
default | \(-\ln \left (x \right )+10 \ln \left (3+\ln \left (x \right )\right )\) | \(13\) |
norman | \(-\ln \left (x \right )+10 \ln \left (3+\ln \left (x \right )\right )\) | \(13\) |
risch | \(-\ln \left (x \right )+10 \ln \left (3+\ln \left (x \right )\right )\) | \(13\) |
parallelrisch | \(-\ln \left (x \right )+10 \ln \left (3+\ln \left (x \right )\right )\) | \(13\) |
[In]
[Out]
none
Time = 0.31 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {7-\log (x)}{x (3+\log (x))} \, dx=-\log \left (x\right ) + 10 \, \log \left (\log \left (x\right ) + 3\right ) \]
[In]
[Out]
Time = 0.05 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {7-\log (x)}{x (3+\log (x))} \, dx=- \log {\left (x \right )} + 10 \log {\left (\log {\left (x \right )} + 3 \right )} \]
[In]
[Out]
none
Time = 0.20 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {7-\log (x)}{x (3+\log (x))} \, dx=-\log \left (x\right ) + 10 \, \log \left (\log \left (x\right ) + 3\right ) \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 27 vs. \(2 (12) = 24\).
Time = 0.29 (sec) , antiderivative size = 27, normalized size of antiderivative = 2.25 \[ \int \frac {7-\log (x)}{x (3+\log (x))} \, dx=5 \, \log \left (\frac {1}{4} \, \pi ^{2} {\left (\mathrm {sgn}\left (x\right ) - 1\right )}^{2} + {\left (\log \left ({\left | x \right |}\right ) + 3\right )}^{2}\right ) - \log \left (x\right ) \]
[In]
[Out]
Time = 1.44 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {7-\log (x)}{x (3+\log (x))} \, dx=10\,\ln \left (\ln \left (x\right )+3\right )-\ln \left (x\right ) \]
[In]
[Out]