Optimal. Leaf size=27 \[ 3 \left (e^4+16 x^2-\frac {2}{2+\left (-3+(-4+x)^2\right ) \log (x)}\right ) \]
________________________________________________________________________________________
Rubi [F] time = 2.75, 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 {78-48 x+390 x^2+\left (-48 x+5004 x^2-3072 x^3+384 x^4\right ) \log (x)+\left (16224 x^2-19968 x^3+8640 x^4-1536 x^5+96 x^6\right ) \log ^2(x)}{4 x+\left (52 x-32 x^2+4 x^3\right ) \log (x)+\left (169 x-208 x^2+90 x^3-16 x^4+x^5\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 {6 \left (13-8 x+65 x^2+2 x \left (-4+417 x-256 x^2+32 x^3\right ) \log (x)+16 x^2 \left (13-8 x+x^2\right )^2 \log ^2(x)\right )}{x \left (2+\left (13-8 x+x^2\right ) \log (x)\right )^2} \, dx\\ &=6 \int \frac {13-8 x+65 x^2+2 x \left (-4+417 x-256 x^2+32 x^3\right ) \log (x)+16 x^2 \left (13-8 x+x^2\right )^2 \log ^2(x)}{x \left (2+\left (13-8 x+x^2\right ) \log (x)\right )^2} \, dx\\ &=6 \int \left (16 x+\frac {169-192 x+86 x^2-16 x^3+x^4}{x \left (13-8 x+x^2\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2}+\frac {2 (-4+x)}{\left (13-8 x+x^2\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )}\right ) \, dx\\ &=48 x^2+6 \int \frac {169-192 x+86 x^2-16 x^3+x^4}{x \left (13-8 x+x^2\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2} \, dx+12 \int \frac {-4+x}{\left (13-8 x+x^2\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )} \, dx\\ &=48 x^2+6 \int \left (-\frac {8}{\left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2}+\frac {13}{x \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2}+\frac {x}{\left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2}-\frac {4 (-4+x)}{\left (13-8 x+x^2\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2}\right ) \, dx+12 \int \left (-\frac {4}{\left (13-8 x+x^2\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )}+\frac {x}{\left (13-8 x+x^2\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )}\right ) \, dx\\ &=48 x^2+6 \int \frac {x}{\left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2} \, dx+12 \int \frac {x}{\left (13-8 x+x^2\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )} \, dx-24 \int \frac {-4+x}{\left (13-8 x+x^2\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2} \, dx-48 \int \frac {1}{\left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2} \, dx-48 \int \frac {1}{\left (13-8 x+x^2\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )} \, dx+78 \int \frac {1}{x \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2} \, dx\\ &=48 x^2+6 \int \frac {x}{\left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2} \, dx+12 \int \left (\frac {1+\frac {4}{\sqrt {3}}}{\left (-8-2 \sqrt {3}+2 x\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )}+\frac {1-\frac {4}{\sqrt {3}}}{\left (-8+2 \sqrt {3}+2 x\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )}\right ) \, dx-24 \int \left (-\frac {4}{\left (13-8 x+x^2\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2}+\frac {x}{\left (13-8 x+x^2\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2}\right ) \, dx-48 \int \frac {1}{\left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2} \, dx-48 \int \left (-\frac {1}{\sqrt {3} \left (8+2 \sqrt {3}-2 x\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )}-\frac {1}{\sqrt {3} \left (-8+2 \sqrt {3}+2 x\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )}\right ) \, dx+78 \int \frac {1}{x \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2} \, dx\\ &=48 x^2+6 \int \frac {x}{\left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2} \, dx-24 \int \frac {x}{\left (13-8 x+x^2\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2} \, dx-48 \int \frac {1}{\left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2} \, dx+78 \int \frac {1}{x \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2} \, dx+96 \int \frac {1}{\left (13-8 x+x^2\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2} \, dx+\left (16 \sqrt {3}\right ) \int \frac {1}{\left (8+2 \sqrt {3}-2 x\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )} \, dx+\left (16 \sqrt {3}\right ) \int \frac {1}{\left (-8+2 \sqrt {3}+2 x\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )} \, dx+\left (4 \left (3-4 \sqrt {3}\right )\right ) \int \frac {1}{\left (-8+2 \sqrt {3}+2 x\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )} \, dx+\left (4 \left (3+4 \sqrt {3}\right )\right ) \int \frac {1}{\left (-8-2 \sqrt {3}+2 x\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )} \, dx\\ &=48 x^2+6 \int \frac {x}{\left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2} \, dx-24 \int \left (\frac {1+\frac {4}{\sqrt {3}}}{\left (-8-2 \sqrt {3}+2 x\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2}+\frac {1-\frac {4}{\sqrt {3}}}{\left (-8+2 \sqrt {3}+2 x\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2}\right ) \, dx-48 \int \frac {1}{\left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2} \, dx+78 \int \frac {1}{x \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2} \, dx+96 \int \left (-\frac {1}{\sqrt {3} \left (8+2 \sqrt {3}-2 x\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2}-\frac {1}{\sqrt {3} \left (-8+2 \sqrt {3}+2 x\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2}\right ) \, dx+\left (16 \sqrt {3}\right ) \int \frac {1}{\left (8+2 \sqrt {3}-2 x\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )} \, dx+\left (16 \sqrt {3}\right ) \int \frac {1}{\left (-8+2 \sqrt {3}+2 x\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )} \, dx+\left (4 \left (3-4 \sqrt {3}\right )\right ) \int \frac {1}{\left (-8+2 \sqrt {3}+2 x\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )} \, dx+\left (4 \left (3+4 \sqrt {3}\right )\right ) \int \frac {1}{\left (-8-2 \sqrt {3}+2 x\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )} \, dx\\ &=48 x^2+6 \int \frac {x}{\left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2} \, dx-48 \int \frac {1}{\left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2} \, dx+78 \int \frac {1}{x \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2} \, dx+\left (16 \sqrt {3}\right ) \int \frac {1}{\left (8+2 \sqrt {3}-2 x\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )} \, dx+\left (16 \sqrt {3}\right ) \int \frac {1}{\left (-8+2 \sqrt {3}+2 x\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )} \, dx-\left (32 \sqrt {3}\right ) \int \frac {1}{\left (8+2 \sqrt {3}-2 x\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2} \, dx-\left (32 \sqrt {3}\right ) \int \frac {1}{\left (-8+2 \sqrt {3}+2 x\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2} \, dx+\left (4 \left (3-4 \sqrt {3}\right )\right ) \int \frac {1}{\left (-8+2 \sqrt {3}+2 x\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )} \, dx-\left (8 \left (3-4 \sqrt {3}\right )\right ) \int \frac {1}{\left (-8+2 \sqrt {3}+2 x\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2} \, dx+\left (4 \left (3+4 \sqrt {3}\right )\right ) \int \frac {1}{\left (-8-2 \sqrt {3}+2 x\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )} \, dx-\left (8 \left (3+4 \sqrt {3}\right )\right ) \int \frac {1}{\left (-8-2 \sqrt {3}+2 x\right ) \left (2+13 \log (x)-8 x \log (x)+x^2 \log (x)\right )^2} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.43, size = 25, normalized size = 0.93 \begin {gather*} 6 \left (8 x^2-\frac {1}{2+\left (13-8 x+x^2\right ) \log (x)}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.47, size = 42, normalized size = 1.56 \begin {gather*} \frac {6 \, {\left (16 \, x^{2} + 8 \, {\left (x^{4} - 8 \, x^{3} + 13 \, x^{2}\right )} \log \relax (x) - 1\right )}}{{\left (x^{2} - 8 \, x + 13\right )} \log \relax (x) + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.31, size = 27, normalized size = 1.00 \begin {gather*} 48 \, x^{2} - \frac {6}{x^{2} \log \relax (x) - 8 \, x \log \relax (x) + 13 \, \log \relax (x) + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.06, size = 28, normalized size = 1.04
method | result | size |
risch | \(48 x^{2}-\frac {6}{x^{2} \ln \relax (x )-8 x \ln \relax (x )+13 \ln \relax (x )+2}\) | \(28\) |
norman | \(\frac {39 \ln \relax (x )-24 x \ln \relax (x )+627 x^{2} \ln \relax (x )+96 x^{2}-384 x^{3} \ln \relax (x )+48 x^{4} \ln \relax (x )}{x^{2} \ln \relax (x )-8 x \ln \relax (x )+13 \ln \relax (x )+2}\) | \(57\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.57, size = 42, normalized size = 1.56 \begin {gather*} \frac {6 \, {\left (16 \, x^{2} + 8 \, {\left (x^{4} - 8 \, x^{3} + 13 \, x^{2}\right )} \log \relax (x) - 1\right )}}{{\left (x^{2} - 8 \, x + 13\right )} \log \relax (x) + 2} \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)}^2\,\left (96\,x^6-1536\,x^5+8640\,x^4-19968\,x^3+16224\,x^2\right )-48\,x-\ln \relax (x)\,\left (-384\,x^4+3072\,x^3-5004\,x^2+48\,x\right )+390\,x^2+78}{\left (x^5-16\,x^4+90\,x^3-208\,x^2+169\,x\right )\,{\ln \relax (x)}^2+\left (4\,x^3-32\,x^2+52\,x\right )\,\ln \relax (x)+4\,x} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.20, size = 19, normalized size = 0.70 \begin {gather*} 48 x^{2} - \frac {6}{\left (x^{2} - 8 x + 13\right ) \log {\relax (x )} + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________