Optimal. Leaf size=20 \[ \frac {2 \left (8+\frac {1}{81 x^2 \log ^2(x)}\right )}{1+x} \]
________________________________________________________________________________________
Rubi [F] time = 0.42, 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 {-4-4 x+(-4-6 x) \log (x)-1296 x^3 \log ^3(x)}{\left (81 x^3+162 x^4+81 x^5\right ) \log ^3(x)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-4-4 x+(-4-6 x) \log (x)-1296 x^3 \log ^3(x)}{x^3 \left (81+162 x+81 x^2\right ) \log ^3(x)} \, dx\\ &=\int \frac {-4-4 x+(-4-6 x) \log (x)-1296 x^3 \log ^3(x)}{81 x^3 (1+x)^2 \log ^3(x)} \, dx\\ &=\frac {1}{81} \int \frac {-4-4 x+(-4-6 x) \log (x)-1296 x^3 \log ^3(x)}{x^3 (1+x)^2 \log ^3(x)} \, dx\\ &=\frac {1}{81} \int \left (-\frac {1296}{(1+x)^2}-\frac {4}{x^3 (1+x) \log ^3(x)}-\frac {2 (2+3 x)}{x^3 (1+x)^2 \log ^2(x)}\right ) \, dx\\ &=\frac {16}{1+x}-\frac {2}{81} \int \frac {2+3 x}{x^3 (1+x)^2 \log ^2(x)} \, dx-\frac {4}{81} \int \frac {1}{x^3 (1+x) \log ^3(x)} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.13, size = 19, normalized size = 0.95 \begin {gather*} \frac {2 \left (648+\frac {1}{x^2 \log ^2(x)}\right )}{81 (1+x)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.56, size = 26, normalized size = 1.30 \begin {gather*} \frac {2 \, {\left (648 \, x^{2} \log \relax (x)^{2} + 1\right )}}{81 \, {\left (x^{3} + x^{2}\right )} \log \relax (x)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.24, size = 29, normalized size = 1.45 \begin {gather*} \frac {2}{81 \, {\left (x^{3} \log \relax (x)^{2} + x^{2} \log \relax (x)^{2}\right )}} + \frac {16}{x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.04, size = 23, normalized size = 1.15
method | result | size |
risch | \(\frac {16}{x +1}+\frac {2}{81 x^{2} \left (x +1\right ) \ln \relax (x )^{2}}\) | \(23\) |
norman | \(\frac {\frac {2}{81}+16 x^{2} \ln \relax (x )^{2}}{x^{2} \left (x +1\right ) \ln \relax (x )^{2}}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.44, size = 26, normalized size = 1.30 \begin {gather*} \frac {2 \, {\left (648 \, x^{2} \log \relax (x)^{2} + 1\right )}}{81 \, {\left (x^{3} + x^{2}\right )} \log \relax (x)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.83, size = 25, normalized size = 1.25 \begin {gather*} -\frac {16\,x^3\,{\ln \relax (x)}^2-\frac {2}{81}}{x^2\,{\ln \relax (x)}^2\,\left (x+1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.14, size = 20, normalized size = 1.00 \begin {gather*} \frac {2}{\left (81 x^{3} + 81 x^{2}\right ) \log {\relax (x )}^{2}} + \frac {16}{x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________