Optimal. Leaf size=30 \[ \frac {25 \left (1+\frac {1}{3} (5-x) x\right )}{-1+\left (2+(4-\log (x))^2\right )^2} \]
________________________________________________________________________________________
Rubi [F] time = 4.18, 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 {21600+76375 x-23350 x^2+\left (-15000-61000 x+19400 x^2\right ) \log (x)+\left (3600+18500 x-6200 x^2\right ) \log ^2(x)+\left (-300-2500 x+900 x^2\right ) \log ^3(x)+\left (125 x-50 x^2\right ) \log ^4(x)}{312987 x-558144 x \log (x)+442632 x \log ^2(x)-203808 x \log ^3(x)+59586 x \log ^4(x)-11328 x \log ^5(x)+1368 x \log ^6(x)-96 x \log ^7(x)+3 x \log ^8(x)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {21600+76375 x-23350 x^2+\left (-15000-61000 x+19400 x^2\right ) \log (x)+\left (3600+18500 x-6200 x^2\right ) \log ^2(x)+\left (-300-2500 x+900 x^2\right ) \log ^3(x)+\left (125 x-50 x^2\right ) \log ^4(x)}{3 x \left (323-288 \log (x)+100 \log ^2(x)-16 \log ^3(x)+\log ^4(x)\right )^2} \, dx\\ &=\frac {1}{3} \int \frac {21600+76375 x-23350 x^2+\left (-15000-61000 x+19400 x^2\right ) \log (x)+\left (3600+18500 x-6200 x^2\right ) \log ^2(x)+\left (-300-2500 x+900 x^2\right ) \log ^3(x)+\left (125 x-50 x^2\right ) \log ^4(x)}{x \left (323-288 \log (x)+100 \log ^2(x)-16 \log ^3(x)+\log ^4(x)\right )^2} \, dx\\ &=\frac {1}{3} \int \left (\frac {25 \left (-3-5 x+x^2\right ) (-4+\log (x))}{x \left (17-8 \log (x)+\log ^2(x)\right )^2}-\frac {25 (-5+2 x)}{2 \left (17-8 \log (x)+\log ^2(x)\right )}-\frac {25 \left (-3-5 x+x^2\right ) (-4+\log (x))}{x \left (19-8 \log (x)+\log ^2(x)\right )^2}+\frac {25 (-5+2 x)}{2 \left (19-8 \log (x)+\log ^2(x)\right )}\right ) \, dx\\ &=-\left (\frac {25}{6} \int \frac {-5+2 x}{17-8 \log (x)+\log ^2(x)} \, dx\right )+\frac {25}{6} \int \frac {-5+2 x}{19-8 \log (x)+\log ^2(x)} \, dx+\frac {25}{3} \int \frac {\left (-3-5 x+x^2\right ) (-4+\log (x))}{x \left (17-8 \log (x)+\log ^2(x)\right )^2} \, dx-\frac {25}{3} \int \frac {\left (-3-5 x+x^2\right ) (-4+\log (x))}{x \left (19-8 \log (x)+\log ^2(x)\right )^2} \, dx\\ &=-\left (\frac {25}{6} \int \left (-\frac {5}{17-8 \log (x)+\log ^2(x)}+\frac {2 x}{17-8 \log (x)+\log ^2(x)}\right ) \, dx\right )+\frac {25}{6} \int \left (-\frac {5}{19-8 \log (x)+\log ^2(x)}+\frac {2 x}{19-8 \log (x)+\log ^2(x)}\right ) \, dx+\frac {25}{3} \int \left (-\frac {5 (-4+\log (x))}{\left (17-8 \log (x)+\log ^2(x)\right )^2}-\frac {3 (-4+\log (x))}{x \left (17-8 \log (x)+\log ^2(x)\right )^2}+\frac {x (-4+\log (x))}{\left (17-8 \log (x)+\log ^2(x)\right )^2}\right ) \, dx-\frac {25}{3} \int \left (-\frac {5 (-4+\log (x))}{\left (19-8 \log (x)+\log ^2(x)\right )^2}-\frac {3 (-4+\log (x))}{x \left (19-8 \log (x)+\log ^2(x)\right )^2}+\frac {x (-4+\log (x))}{\left (19-8 \log (x)+\log ^2(x)\right )^2}\right ) \, dx\\ &=\frac {25}{3} \int \frac {x (-4+\log (x))}{\left (17-8 \log (x)+\log ^2(x)\right )^2} \, dx-\frac {25}{3} \int \frac {x}{17-8 \log (x)+\log ^2(x)} \, dx-\frac {25}{3} \int \frac {x (-4+\log (x))}{\left (19-8 \log (x)+\log ^2(x)\right )^2} \, dx+\frac {25}{3} \int \frac {x}{19-8 \log (x)+\log ^2(x)} \, dx+\frac {125}{6} \int \frac {1}{17-8 \log (x)+\log ^2(x)} \, dx-\frac {125}{6} \int \frac {1}{19-8 \log (x)+\log ^2(x)} \, dx-25 \int \frac {-4+\log (x)}{x \left (17-8 \log (x)+\log ^2(x)\right )^2} \, dx+25 \int \frac {-4+\log (x)}{x \left (19-8 \log (x)+\log ^2(x)\right )^2} \, dx-\frac {125}{3} \int \frac {-4+\log (x)}{\left (17-8 \log (x)+\log ^2(x)\right )^2} \, dx+\frac {125}{3} \int \frac {-4+\log (x)}{\left (19-8 \log (x)+\log ^2(x)\right )^2} \, dx\\ &=-\left (\frac {25}{3} \int \frac {x}{17-8 \log (x)+\log ^2(x)} \, dx\right )+\frac {25}{3} \int \frac {x}{19-8 \log (x)+\log ^2(x)} \, dx+\frac {25}{3} \int \left (-\frac {4 x}{\left (17-8 \log (x)+\log ^2(x)\right )^2}+\frac {x \log (x)}{\left (17-8 \log (x)+\log ^2(x)\right )^2}\right ) \, dx-\frac {25}{3} \int \left (-\frac {4 x}{\left (19-8 \log (x)+\log ^2(x)\right )^2}+\frac {x \log (x)}{\left (19-8 \log (x)+\log ^2(x)\right )^2}\right ) \, dx+\frac {125}{6} \int \left (\frac {i}{(8+2 i)-2 \log (x)}+\frac {i}{(-8+2 i)+2 \log (x)}\right ) \, dx-\frac {125}{6} \int \left (\frac {i}{\sqrt {3} \left (8+2 i \sqrt {3}-2 \log (x)\right )}+\frac {i}{\sqrt {3} \left (-8+2 i \sqrt {3}+2 \log (x)\right )}\right ) \, dx-25 \operatorname {Subst}\left (\int \frac {-4+x}{\left (17-8 x+x^2\right )^2} \, dx,x,\log (x)\right )+25 \operatorname {Subst}\left (\int \frac {-4+x}{\left (19-8 x+x^2\right )^2} \, dx,x,\log (x)\right )-\frac {125}{3} \int \left (-\frac {4}{\left (17-8 \log (x)+\log ^2(x)\right )^2}+\frac {\log (x)}{\left (17-8 \log (x)+\log ^2(x)\right )^2}\right ) \, dx+\frac {125}{3} \int \left (-\frac {4}{\left (19-8 \log (x)+\log ^2(x)\right )^2}+\frac {\log (x)}{\left (19-8 \log (x)+\log ^2(x)\right )^2}\right ) \, dx\\ &=\frac {25}{2 \left (17-8 \log (x)+\log ^2(x)\right )}-\frac {25}{2 \left (19-8 \log (x)+\log ^2(x)\right )}+\frac {125}{6} i \int \frac {1}{(8+2 i)-2 \log (x)} \, dx+\frac {125}{6} i \int \frac {1}{(-8+2 i)+2 \log (x)} \, dx+\frac {25}{3} \int \frac {x \log (x)}{\left (17-8 \log (x)+\log ^2(x)\right )^2} \, dx-\frac {25}{3} \int \frac {x}{17-8 \log (x)+\log ^2(x)} \, dx-\frac {25}{3} \int \frac {x \log (x)}{\left (19-8 \log (x)+\log ^2(x)\right )^2} \, dx+\frac {25}{3} \int \frac {x}{19-8 \log (x)+\log ^2(x)} \, dx-\frac {100}{3} \int \frac {x}{\left (17-8 \log (x)+\log ^2(x)\right )^2} \, dx+\frac {100}{3} \int \frac {x}{\left (19-8 \log (x)+\log ^2(x)\right )^2} \, dx-\frac {125}{3} \int \frac {\log (x)}{\left (17-8 \log (x)+\log ^2(x)\right )^2} \, dx+\frac {125}{3} \int \frac {\log (x)}{\left (19-8 \log (x)+\log ^2(x)\right )^2} \, dx+\frac {500}{3} \int \frac {1}{\left (17-8 \log (x)+\log ^2(x)\right )^2} \, dx-\frac {500}{3} \int \frac {1}{\left (19-8 \log (x)+\log ^2(x)\right )^2} \, dx-\frac {(125 i) \int \frac {1}{8+2 i \sqrt {3}-2 \log (x)} \, dx}{6 \sqrt {3}}-\frac {(125 i) \int \frac {1}{-8+2 i \sqrt {3}+2 \log (x)} \, dx}{6 \sqrt {3}}\\ &=\frac {25}{2 \left (17-8 \log (x)+\log ^2(x)\right )}-\frac {25}{2 \left (19-8 \log (x)+\log ^2(x)\right )}+\frac {125}{6} i \operatorname {Subst}\left (\int \frac {e^x}{(8+2 i)-2 x} \, dx,x,\log (x)\right )+\frac {125}{6} i \operatorname {Subst}\left (\int \frac {e^x}{(-8+2 i)+2 x} \, dx,x,\log (x)\right )+\frac {25}{3} \int \frac {x \log (x)}{\left (17-8 \log (x)+\log ^2(x)\right )^2} \, dx-\frac {25}{3} \int \frac {x}{17-8 \log (x)+\log ^2(x)} \, dx-\frac {25}{3} \int \frac {x \log (x)}{\left (19-8 \log (x)+\log ^2(x)\right )^2} \, dx+\frac {25}{3} \int \frac {x}{19-8 \log (x)+\log ^2(x)} \, dx-\frac {100}{3} \int \frac {x}{\left (17-8 \log (x)+\log ^2(x)\right )^2} \, dx+\frac {100}{3} \int \frac {x}{\left (19-8 \log (x)+\log ^2(x)\right )^2} \, dx-\frac {125}{3} \int \left (-\frac {4+i}{((8+2 i)-2 \log (x))^2}+\frac {2 i}{(8+2 i)-2 \log (x)}-\frac {4-i}{((-8+2 i)+2 \log (x))^2}+\frac {2 i}{(-8+2 i)+2 \log (x)}\right ) \, dx+\frac {125}{3} \int \left (-\frac {8+2 i \sqrt {3}}{6 \left (8+2 i \sqrt {3}-2 \log (x)\right )^2}+\frac {2 i}{3 \sqrt {3} \left (8+2 i \sqrt {3}-2 \log (x)\right )}-\frac {8-2 i \sqrt {3}}{6 \left (-8+2 i \sqrt {3}+2 \log (x)\right )^2}+\frac {2 i}{3 \sqrt {3} \left (-8+2 i \sqrt {3}+2 \log (x)\right )}\right ) \, dx+\frac {500}{3} \int \left (-\frac {1}{((8+2 i)-2 \log (x))^2}+\frac {i}{2 ((8+2 i)-2 \log (x))}-\frac {1}{((-8+2 i)+2 \log (x))^2}+\frac {i}{2 ((-8+2 i)+2 \log (x))}\right ) \, dx-\frac {500}{3} \int \left (-\frac {1}{3 \left (8+2 i \sqrt {3}-2 \log (x)\right )^2}+\frac {i}{6 \sqrt {3} \left (8+2 i \sqrt {3}-2 \log (x)\right )}-\frac {1}{3 \left (-8+2 i \sqrt {3}+2 \log (x)\right )^2}+\frac {i}{6 \sqrt {3} \left (-8+2 i \sqrt {3}+2 \log (x)\right )}\right ) \, dx-\frac {(125 i) \operatorname {Subst}\left (\int \frac {e^x}{8+2 i \sqrt {3}-2 x} \, dx,x,\log (x)\right )}{6 \sqrt {3}}-\frac {(125 i) \operatorname {Subst}\left (\int \frac {e^x}{-8+2 i \sqrt {3}+2 x} \, dx,x,\log (x)\right )}{6 \sqrt {3}}\\ &=\frac {125 i e^{4+i \sqrt {3}} \text {Ei}\left (-4-i \sqrt {3}+\log (x)\right )}{12 \sqrt {3}}-\frac {125 i e^{4-i \sqrt {3}} \text {Ei}\left (-4+i \sqrt {3}+\log (x)\right )}{12 \sqrt {3}}-\frac {125}{12} i e^{4+i} \text {Ei}\left (\frac {1}{2} ((-8-2 i)+2 \log (x))\right )+\frac {125}{12} i e^{4-i} \text {Ei}\left (\frac {1}{2} ((-8+2 i)+2 \log (x))\right )+\frac {25}{2 \left (17-8 \log (x)+\log ^2(x)\right )}-\frac {25}{2 \left (19-8 \log (x)+\log ^2(x)\right )}-\left (-\frac {500}{3}-\frac {125 i}{3}\right ) \int \frac {1}{((8+2 i)-2 \log (x))^2} \, dx-\left (-\frac {500}{3}+\frac {125 i}{3}\right ) \int \frac {1}{((-8+2 i)+2 \log (x))^2} \, dx+\frac {25}{3} \int \frac {x \log (x)}{\left (17-8 \log (x)+\log ^2(x)\right )^2} \, dx-\frac {25}{3} \int \frac {x}{17-8 \log (x)+\log ^2(x)} \, dx-\frac {25}{3} \int \frac {x \log (x)}{\left (19-8 \log (x)+\log ^2(x)\right )^2} \, dx+\frac {25}{3} \int \frac {x}{19-8 \log (x)+\log ^2(x)} \, dx-\frac {100}{3} \int \frac {x}{\left (17-8 \log (x)+\log ^2(x)\right )^2} \, dx+\frac {100}{3} \int \frac {x}{\left (19-8 \log (x)+\log ^2(x)\right )^2} \, dx+\frac {500}{9} \int \frac {1}{\left (8+2 i \sqrt {3}-2 \log (x)\right )^2} \, dx+\frac {500}{9} \int \frac {1}{\left (-8+2 i \sqrt {3}+2 \log (x)\right )^2} \, dx-\frac {500}{3} \int \frac {1}{((8+2 i)-2 \log (x))^2} \, dx-\frac {500}{3} \int \frac {1}{((-8+2 i)+2 \log (x))^2} \, dx-\frac {1}{9} \left (125 \left (4-i \sqrt {3}\right )\right ) \int \frac {1}{\left (-8+2 i \sqrt {3}+2 \log (x)\right )^2} \, dx-\frac {1}{9} \left (125 \left (4+i \sqrt {3}\right )\right ) \int \frac {1}{\left (8+2 i \sqrt {3}-2 \log (x)\right )^2} \, dx\\ &=\frac {125 i e^{4+i \sqrt {3}} \text {Ei}\left (-4-i \sqrt {3}+\log (x)\right )}{12 \sqrt {3}}-\frac {125 i e^{4-i \sqrt {3}} \text {Ei}\left (-4+i \sqrt {3}+\log (x)\right )}{12 \sqrt {3}}-\frac {125}{12} i e^{4+i} \text {Ei}\left (\frac {1}{2} ((-8-2 i)+2 \log (x))\right )+\frac {125}{12} i e^{4-i} \text {Ei}\left (\frac {1}{2} ((-8+2 i)+2 \log (x))\right )+\frac {125 i x}{6 ((8+2 i)-2 \log (x))}+\frac {125 x}{9 \left (4-i \sqrt {3}-\log (x)\right )}-\frac {125 \left (4-i \sqrt {3}\right ) x}{36 \left (4-i \sqrt {3}-\log (x)\right )}+\frac {125 x}{9 \left (4+i \sqrt {3}-\log (x)\right )}-\frac {125 \left (4+i \sqrt {3}\right ) x}{36 \left (4+i \sqrt {3}-\log (x)\right )}+\frac {125 i x}{6 ((-8+2 i)+2 \log (x))}+\frac {25}{2 \left (17-8 \log (x)+\log ^2(x)\right )}-\frac {25}{2 \left (19-8 \log (x)+\log ^2(x)\right )}-\left (-\frac {250}{3}+\frac {125 i}{6}\right ) \int \frac {1}{(-8+2 i)+2 \log (x)} \, dx+\frac {25}{3} \int \frac {x \log (x)}{\left (17-8 \log (x)+\log ^2(x)\right )^2} \, dx-\frac {25}{3} \int \frac {x}{17-8 \log (x)+\log ^2(x)} \, dx-\frac {25}{3} \int \frac {x \log (x)}{\left (19-8 \log (x)+\log ^2(x)\right )^2} \, dx+\frac {25}{3} \int \frac {x}{19-8 \log (x)+\log ^2(x)} \, dx-\frac {250}{9} \int \frac {1}{8+2 i \sqrt {3}-2 \log (x)} \, dx+\frac {250}{9} \int \frac {1}{-8+2 i \sqrt {3}+2 \log (x)} \, dx-\frac {100}{3} \int \frac {x}{\left (17-8 \log (x)+\log ^2(x)\right )^2} \, dx+\frac {100}{3} \int \frac {x}{\left (19-8 \log (x)+\log ^2(x)\right )^2} \, dx+\frac {250}{3} \int \frac {1}{(8+2 i)-2 \log (x)} \, dx-\frac {250}{3} \int \frac {1}{(-8+2 i)+2 \log (x)} \, dx-\left (\frac {250}{3}+\frac {125 i}{6}\right ) \int \frac {1}{(8+2 i)-2 \log (x)} \, dx-\frac {1}{18} \left (125 \left (4-i \sqrt {3}\right )\right ) \int \frac {1}{-8+2 i \sqrt {3}+2 \log (x)} \, dx+\frac {1}{18} \left (125 \left (4+i \sqrt {3}\right )\right ) \int \frac {1}{8+2 i \sqrt {3}-2 \log (x)} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.04, size = 36, normalized size = 1.20 \begin {gather*} -\frac {25 \left (-3-5 x+x^2\right )}{3 \left (323-288 \log (x)+100 \log ^2(x)-16 \log ^3(x)+\log ^4(x)\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.52, size = 34, normalized size = 1.13 \begin {gather*} -\frac {25 \, {\left (x^{2} - 5 \, x - 3\right )}}{3 \, {\left (\log \relax (x)^{4} - 16 \, \log \relax (x)^{3} + 100 \, \log \relax (x)^{2} - 288 \, \log \relax (x) + 323\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.18, size = 34, normalized size = 1.13 \begin {gather*} -\frac {25 \, {\left (x^{2} - 5 \, x - 3\right )}}{3 \, {\left (\log \relax (x)^{4} - 16 \, \log \relax (x)^{3} + 100 \, \log \relax (x)^{2} - 288 \, \log \relax (x) + 323\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.02, size = 35, normalized size = 1.17
method | result | size |
risch | \(-\frac {25 \left (x^{2}-5 x -3\right )}{3 \left (\ln \relax (x )^{4}-16 \ln \relax (x )^{3}+100 \ln \relax (x )^{2}-288 \ln \relax (x )+323\right )}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.42, size = 34, normalized size = 1.13 \begin {gather*} -\frac {25 \, {\left (x^{2} - 5 \, x - 3\right )}}{3 \, {\left (\log \relax (x)^{4} - 16 \, \log \relax (x)^{3} + 100 \, \log \relax (x)^{2} - 288 \, \log \relax (x) + 323\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 4.41, size = 48, normalized size = 1.60 \begin {gather*} \frac {-\frac {25\,x^2}{6}+\frac {125\,x}{6}+\frac {25}{2}}{{\ln \relax (x)}^2-8\,\ln \relax (x)+17}-\frac {-\frac {25\,x^2}{6}+\frac {125\,x}{6}+\frac {25}{2}}{{\ln \relax (x)}^2-8\,\ln \relax (x)+19} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.18, size = 36, normalized size = 1.20 \begin {gather*} \frac {- 25 x^{2} + 125 x + 75}{3 \log {\relax (x )}^{4} - 48 \log {\relax (x )}^{3} + 300 \log {\relax (x )}^{2} - 864 \log {\relax (x )} + 969} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________