\[ \int \frac {\left (-12 x^7+4 x^9+\left (12 x^6-8 x^8\right ) \log (4)\right ) \log ^3\left (\frac {5 x-5 \log (4)}{x^2}\right )+\left (-8 x^9+8 x^8 \log (4)\right ) \log ^4\left (\frac {5 x-5 \log (4)}{x^2}\right )+\log ^3(x) \left (-324 x+108 x^3+\left (324-216 x^2\right ) \log (4)+\left (-216 x^3+216 x^2 \log (4)\right ) \log \left (\frac {5 x-5 \log (4)}{x^2}\right )\right )+\log ^2(x) \left (\left (-324 x^3+108 x^5+\left (324 x^2-216 x^4\right ) \log (4)\right ) \log \left (\frac {5 x-5 \log (4)}{x^2}\right )+\left (-216 x^5+216 x^4 \log (4)\right ) \log ^2\left (\frac {5 x-5 \log (4)}{x^2}\right )\right )+\log (x) \left (\left (-108 x^5+36 x^7+\left (108 x^4-72 x^6\right ) \log (4)\right ) \log ^2\left (\frac {5 x-5 \log (4)}{x^2}\right )+\left (-72 x^7+72 x^6 \log (4)\right ) \log ^3\left (\frac {5 x-5 \log (4)}{x^2}\right )\right )}{-81 x^2+81 x \log (4)} \, dx \]
Optimal antiderivative \[ \left (\ln \! \left (x \right )+\frac {\ln \! \left (\frac {5}{x}-\frac {10 \ln \left (2\right )}{x^{2}}\right ) x^{2}}{3}\right )^{4} \]
command
int((((432*x^2*ln(2)-216*x^3)*ln((-10*ln(2)+5*x)/x^2)+2*(-216*x^2+324)*ln(2)+108*x^3-324*x)*ln(x)^3+((432*x^4*ln(2)-216*x^5)*ln((-10*ln(2)+5*x)/x^2)^2+(2*(-216*x^4+324*x^2)*ln(2)+108*x^5-324*x^3)*ln((-10*ln(2)+5*x)/x^2))*ln(x)^2+((144*x^6*ln(2)-72*x^7)*ln((-10*ln(2)+5*x)/x^2)^3+(2*(-72*x^6+108*x^4)*ln(2)+36*x^7-108*x^5)*ln((-10*ln(2)+5*x)/x^2)^2)*ln(x)+(16*x^8*ln(2)-8*x^9)*ln((-10*ln(2)+5*x)/x^2)^4+(2*(-8*x^8+12*x^6)*ln(2)+4*x^9-12*x^7)*ln((-10*ln(2)+5*x)/x^2)^3)/(162*x*ln(2)-81*x^2),x)
Maple 2022.1 output
\[\int \frac {\left (\left (432 x^{2} \ln \left (2\right )-216 x^{3}\right ) \ln \left (\frac {-10 \ln \left (2\right )+5 x}{x^{2}}\right )+2 \left (-216 x^{2}+324\right ) \ln \left (2\right )+108 x^{3}-324 x \right ) \ln \left (x \right )^{3}+\left (\left (432 x^{4} \ln \left (2\right )-216 x^{5}\right ) \ln \left (\frac {-10 \ln \left (2\right )+5 x}{x^{2}}\right )^{2}+\left (2 \left (-216 x^{4}+324 x^{2}\right ) \ln \left (2\right )+108 x^{5}-324 x^{3}\right ) \ln \left (\frac {-10 \ln \left (2\right )+5 x}{x^{2}}\right )\right ) \ln \left (x \right )^{2}+\left (\left (144 x^{6} \ln \left (2\right )-72 x^{7}\right ) \ln \left (\frac {-10 \ln \left (2\right )+5 x}{x^{2}}\right )^{3}+\left (2 \left (-72 x^{6}+108 x^{4}\right ) \ln \left (2\right )+36 x^{7}-108 x^{5}\right ) \ln \left (\frac {-10 \ln \left (2\right )+5 x}{x^{2}}\right )^{2}\right ) \ln \left (x \right )+\left (16 x^{8} \ln \left (2\right )-8 x^{9}\right ) \ln \left (\frac {-10 \ln \left (2\right )+5 x}{x^{2}}\right )^{4}+\left (2 \left (-8 x^{8}+12 x^{6}\right ) \ln \left (2\right )+4 x^{9}-12 x^{7}\right ) \ln \left (\frac {-10 \ln \left (2\right )+5 x}{x^{2}}\right )^{3}}{162 x \ln \left (2\right )-81 x^{2}}\, dx\]
Maple 2021.1 output
| method | result | size |
| risch | \(\text {Expression too large to display}\) | \(77075\) |