Optimal. Leaf size=27 \[ \frac {x}{(1-x) \left (x+81 x^2-\log (x)-x \log (x)\right )} \]
________________________________________________________________________________________
Rubi [F] time = 1.30, 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 {1-81 x^2+162 x^3+\left (-1-x^2\right ) \log (x)}{x^2+160 x^3+6238 x^4-12960 x^5+6561 x^6+\left (-2 x-160 x^2+164 x^3+160 x^4-162 x^5\right ) \log (x)+\left (1-2 x^2+x^4\right ) \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 {1-81 x^2+162 x^3-\left (1+x^2\right ) \log (x)}{(1-x)^2 (x (1+81 x)-(1+x) \log (x))^2} \, dx\\ &=\int \left (\frac {-1-x+161 x^2+81 x^3}{\left (-1+x^2\right ) \left (x+81 x^2-\log (x)-x \log (x)\right )^2}+\frac {1+x^2}{(-1+x)^2 (1+x) \left (x+81 x^2-\log (x)-x \log (x)\right )}\right ) \, dx\\ &=\int \frac {-1-x+161 x^2+81 x^3}{\left (-1+x^2\right ) \left (x+81 x^2-\log (x)-x \log (x)\right )^2} \, dx+\int \frac {1+x^2}{(-1+x)^2 (1+x) \left (x+81 x^2-\log (x)-x \log (x)\right )} \, dx\\ &=\int \left (\frac {161}{\left (x+81 x^2-\log (x)-x \log (x)\right )^2}+\frac {120}{(-1+x) \left (x+81 x^2-\log (x)-x \log (x)\right )^2}+\frac {81 x}{\left (x+81 x^2-\log (x)-x \log (x)\right )^2}-\frac {40}{(1+x) \left (x+81 x^2-\log (x)-x \log (x)\right )^2}\right ) \, dx+\int \left (\frac {1}{(-1+x)^2 \left (x+81 x^2-\log (x)-x \log (x)\right )}+\frac {1}{2 (-1+x) \left (x+81 x^2-\log (x)-x \log (x)\right )}+\frac {1}{2 (1+x) \left (x+81 x^2-\log (x)-x \log (x)\right )}\right ) \, dx\\ &=\frac {1}{2} \int \frac {1}{(-1+x) \left (x+81 x^2-\log (x)-x \log (x)\right )} \, dx+\frac {1}{2} \int \frac {1}{(1+x) \left (x+81 x^2-\log (x)-x \log (x)\right )} \, dx-40 \int \frac {1}{(1+x) \left (x+81 x^2-\log (x)-x \log (x)\right )^2} \, dx+81 \int \frac {x}{\left (x+81 x^2-\log (x)-x \log (x)\right )^2} \, dx+120 \int \frac {1}{(-1+x) \left (x+81 x^2-\log (x)-x \log (x)\right )^2} \, dx+161 \int \frac {1}{\left (x+81 x^2-\log (x)-x \log (x)\right )^2} \, dx+\int \frac {1}{(-1+x)^2 \left (x+81 x^2-\log (x)-x \log (x)\right )} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.41, size = 24, normalized size = 0.89 \begin {gather*} \frac {x}{(-1+x) \left (-x-81 x^2+\log (x)+x \log (x)\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.64, size = 28, normalized size = 1.04 \begin {gather*} -\frac {x}{81 \, x^{3} - 80 \, x^{2} - {\left (x^{2} - 1\right )} \log \relax (x) - x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.17, size = 28, normalized size = 1.04 \begin {gather*} -\frac {x}{81 \, x^{3} - x^{2} \log \relax (x) - 80 \, x^{2} - x + \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.08, size = 27, normalized size = 1.00
method | result | size |
risch | \(-\frac {x}{\left (x -1\right ) \left (81 x^{2}-\ln \relax (x )-x \ln \relax (x )+x \right )}\) | \(27\) |
norman | \(-\frac {x}{81 x^{3}-x^{2} \ln \relax (x )-80 x^{2}-x +\ln \relax (x )}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.41, size = 28, normalized size = 1.04 \begin {gather*} -\frac {x}{81 \, x^{3} - 80 \, x^{2} - {\left (x^{2} - 1\right )} \log \relax (x) - x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {\ln \relax (x)\,\left (x^2+1\right )+81\,x^2-162\,x^3-1}{{\ln \relax (x)}^2\,\left (x^4-2\,x^2+1\right )-\ln \relax (x)\,\left (162\,x^5-160\,x^4-164\,x^3+160\,x^2+2\,x\right )+x^2+160\,x^3+6238\,x^4-12960\,x^5+6561\,x^6} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.22, size = 20, normalized size = 0.74 \begin {gather*} \frac {x}{- 81 x^{3} + 80 x^{2} + x + \left (x^{2} - 1\right ) \log {\relax (x )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________