Problem number 5812

20.2 Problem number 5812

$\int \frac{(- 12 x^{7} + 4 x^{9} + (12 x^{6} - 8 x^{8}) \log (4)) \log^{3} (\frac{5 x - 5 \log (4)}{x^{2}}) + (- 8 x^{9} + 8 x^{8} \log (4)) \log^{4} (\frac{5 x - 5 \log (4)}{x^{2}}) + \log^{3} (x) (- 324 x + 108 x^{3} + (324 - 216 x^{2}) \log (4) + (- 216 x^{3} + 216 x^{2} \log (4)) \log (\frac{5 x - 5 \log (4)}{x^{2}})) + \log^{2} (x) ((- 324 x^{3} + 108 x^{5} + (324 x^{2} - 216 x^{4}) \log (4)) \log (\frac{5 x - 5 \log (4)}{x^{2}}) + (- 216 x^{5} + 216 x^{4} \log (4)) \log^{2} (\frac{5 x - 5 \log (4)}{x^{2}})) + \log (x) ((- 108 x^{5} + 36 x^{7} + (108 x^{4} - 72 x^{6}) \log (4)) \log^{2} (\frac{5 x - 5 \log (4)}{x^{2}}) + (- 72 x^{7} + 72 x^{6} \log (4)) \log^{3} (\frac{5 x - 5 \log (4)}{x^{2}}))}{- 81 x^{2} + 81 x \log (4)} d x$

Optimal antiderivative ${(\ln (x) + \frac{\ln (\frac{5}{x} - \frac{10 \ln (2)}{x^{2}}) x^{2}}{3})}^{4}$

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

$\int \frac{((432 x^{2} \ln (2) - 216 x^{3}) \ln (\frac{- 10 \ln (2) + 5 x}{x^{2}}) + 2 (- 216 x^{2} + 324) \ln (2) + 108 x^{3} - 324 x) \ln {(x)}^{3} + ((432 x^{4} \ln (2) - 216 x^{5}) \ln {(\frac{- 10 \ln (2) + 5 x}{x^{2}})}^{2} + (2 (- 216 x^{4} + 324 x^{2}) \ln (2) + 108 x^{5} - 324 x^{3}) \ln (\frac{- 10 \ln (2) + 5 x}{x^{2}})) \ln {(x)}^{2} + ((144 x^{6} \ln (2) - 72 x^{7}) \ln {(\frac{- 10 \ln (2) + 5 x}{x^{2}})}^{3} + (2 (- 72 x^{6} + 108 x^{4}) \ln (2) + 36 x^{7} - 108 x^{5}) \ln {(\frac{- 10 \ln (2) + 5 x}{x^{2}})}^{2}) \ln (x) + (16 x^{8} \ln (2) - 8 x^{9}) \ln {(\frac{- 10 \ln (2) + 5 x}{x^{2}})}^{4} + (2 (- 8 x^{8} + 12 x^{6}) \ln (2) + 4 x^{9} - 12 x^{7}) \ln {(\frac{- 10 \ln (2) + 5 x}{x^{2}})}^{3}}{162 x \ln (2) - 81 x^{2}} d x$

Maple 2021.1 output


method	result	size

risch	$Expression too large to display$	$77075$

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