Optimal. Leaf size=19 \[ -\frac {1}{x-\frac {\log (x)}{\frac {2}{3}-2 x}} \]
________________________________________________________________________________________
Rubi [F] time = 0.66, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {-6+22 x-24 x^2+36 x^3-18 x \log (x)}{4 x^3-24 x^4+36 x^5+\left (-12 x^2+36 x^3\right ) \log (x)+9 x \log ^2(x)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \left (-3+11 x-12 x^2+18 x^3-9 x \log (x)\right )}{x (2 x (-1+3 x)+3 \log (x))^2} \, dx\\ &=2 \int \frac {-3+11 x-12 x^2+18 x^3-9 x \log (x)}{x (2 x (-1+3 x)+3 \log (x))^2} \, dx\\ &=2 \int \left (\frac {-3+11 x-18 x^2+36 x^3}{x \left (-2 x+6 x^2+3 \log (x)\right )^2}-\frac {3}{-2 x+6 x^2+3 \log (x)}\right ) \, dx\\ &=2 \int \frac {-3+11 x-18 x^2+36 x^3}{x \left (-2 x+6 x^2+3 \log (x)\right )^2} \, dx-6 \int \frac {1}{-2 x+6 x^2+3 \log (x)} \, dx\\ &=2 \int \left (\frac {11}{\left (-2 x+6 x^2+3 \log (x)\right )^2}-\frac {3}{x \left (-2 x+6 x^2+3 \log (x)\right )^2}-\frac {18 x}{\left (-2 x+6 x^2+3 \log (x)\right )^2}+\frac {36 x^2}{\left (-2 x+6 x^2+3 \log (x)\right )^2}\right ) \, dx-6 \int \frac {1}{-2 x+6 x^2+3 \log (x)} \, dx\\ &=-\left (6 \int \frac {1}{x \left (-2 x+6 x^2+3 \log (x)\right )^2} \, dx\right )-6 \int \frac {1}{-2 x+6 x^2+3 \log (x)} \, dx+22 \int \frac {1}{\left (-2 x+6 x^2+3 \log (x)\right )^2} \, dx-36 \int \frac {x}{\left (-2 x+6 x^2+3 \log (x)\right )^2} \, dx+72 \int \frac {x^2}{\left (-2 x+6 x^2+3 \log (x)\right )^2} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.28, size = 22, normalized size = 1.16 \begin {gather*} \frac {2 (1-3 x)}{-2 x+6 x^2+3 \log (x)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.02, size = 22, normalized size = 1.16 \begin {gather*} -\frac {2 \, {\left (3 \, x - 1\right )}}{6 \, x^{2} - 2 \, x + 3 \, \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.13, size = 22, normalized size = 1.16 \begin {gather*} -\frac {2 \, {\left (3 \, x - 1\right )}}{6 \, x^{2} - 2 \, x + 3 \, \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.04, size = 22, normalized size = 1.16
method | result | size |
norman | \(\frac {-6 x +2}{6 x^{2}+3 \ln \relax (x )-2 x}\) | \(22\) |
risch | \(-\frac {2 \left (3 x -1\right )}{6 x^{2}+3 \ln \relax (x )-2 x}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.40, size = 22, normalized size = 1.16 \begin {gather*} -\frac {2 \, {\left (3 \, x - 1\right )}}{6 \, x^{2} - 2 \, x + 3 \, \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 5.45, size = 22, normalized size = 1.16 \begin {gather*} -\frac {6\,x-2}{3\,\ln \relax (x)-2\,x+6\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.12, size = 17, normalized size = 0.89 \begin {gather*} \frac {2 - 6 x}{6 x^{2} - 2 x + 3 \log {\relax (x )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________