Integrand size = 28, antiderivative size = 27 \[ \int \frac {-20+360 x-270 x^2+15 x \log (x)}{-18 x^2+x \log (x)} \, dx=5 \left (-4+x-2 \left (5-x+\log \left (\left (-\frac {9 x}{2}+\frac {\log (x)}{4}\right )^2\right )\right )\right ) \]
[Out]
Time = 0.22 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.56, number of steps used = 6, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.179, Rules used = {2641, 6873, 12, 6874, 6816} \[ \int \frac {-20+360 x-270 x^2+15 x \log (x)}{-18 x^2+x \log (x)} \, dx=15 x-20 \log (18 x-\log (x)) \]
[In]
[Out]
Rule 12
Rule 2641
Rule 6816
Rule 6873
Rule 6874
Rubi steps \begin{align*} \text {integral}& = \int \frac {-20+360 x-270 x^2+15 x \log (x)}{x (-18 x+\log (x))} \, dx \\ & = \int \frac {5 \left (4-72 x+54 x^2-3 x \log (x)\right )}{x (18 x-\log (x))} \, dx \\ & = 5 \int \frac {4-72 x+54 x^2-3 x \log (x)}{x (18 x-\log (x))} \, dx \\ & = 5 \int \left (3-\frac {4 (-1+18 x)}{x (18 x-\log (x))}\right ) \, dx \\ & = 15 x-20 \int \frac {-1+18 x}{x (18 x-\log (x))} \, dx \\ & = 15 x-20 \log (18 x-\log (x)) \\ \end{align*}
Time = 0.06 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.63 \[ \int \frac {-20+360 x-270 x^2+15 x \log (x)}{-18 x^2+x \log (x)} \, dx=5 (3 x-4 \log (18 x-\log (x))) \]
[In]
[Out]
Time = 0.20 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.52
method | result | size |
default | \(15 x -20 \ln \left (\ln \left (x \right )-18 x \right )\) | \(14\) |
risch | \(15 x -20 \ln \left (\ln \left (x \right )-18 x \right )\) | \(14\) |
parallelrisch | \(-20 \ln \left (-\frac {\ln \left (x \right )}{18}+x \right )+15 x\) | \(14\) |
norman | \(15 x -20 \ln \left (18 x -\ln \left (x \right )\right )\) | \(16\) |
[In]
[Out]
none
Time = 0.25 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.48 \[ \int \frac {-20+360 x-270 x^2+15 x \log (x)}{-18 x^2+x \log (x)} \, dx=15 \, x - 20 \, \log \left (-18 \, x + \log \left (x\right )\right ) \]
[In]
[Out]
Time = 0.06 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.44 \[ \int \frac {-20+360 x-270 x^2+15 x \log (x)}{-18 x^2+x \log (x)} \, dx=15 x - 20 \log {\left (- 18 x + \log {\left (x \right )} \right )} \]
[In]
[Out]
none
Time = 0.22 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.48 \[ \int \frac {-20+360 x-270 x^2+15 x \log (x)}{-18 x^2+x \log (x)} \, dx=15 \, x - 20 \, \log \left (-18 \, x + \log \left (x\right )\right ) \]
[In]
[Out]
none
Time = 0.25 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.56 \[ \int \frac {-20+360 x-270 x^2+15 x \log (x)}{-18 x^2+x \log (x)} \, dx=15 \, x - 20 \, \log \left (18 \, x - \log \left (x\right )\right ) \]
[In]
[Out]
Time = 8.44 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.56 \[ \int \frac {-20+360 x-270 x^2+15 x \log (x)}{-18 x^2+x \log (x)} \, dx=15\,x-20\,\ln \left (18\,x-\ln \left (x\right )\right ) \]
[In]
[Out]