Problem number 7552

20.5 Problem number 7552

$\int \frac{- 1 - x + e^{5 x} (1 + x) + (2 - 2 e^{5 x}) \log (x) + (- x + e^{5 x} x + (1 - e^{5 x}) \log (x)) \log (- x + \log (x)) + (2 x + e^{5 x} (- 2 x - 10 x^{2}) + (- 2 + e^{5 x} (2 + 10 x)) \log (x) + (x + e^{5 x} (- x - 5 x^{2}) + (- 1 + e^{5 x} (1 + 5 x)) \log (x)) \log (- x + \log (x))) \log (- \frac{x}{2 + \log (- x + \log (x))})}{(- 2 x + 2 \log (x) + (- x + \log (x)) \log (- x + \log (x))) \log^{2} (- \frac{x}{2 + \log (- x + \log (x))})} d x$

Optimal antiderivative $1 + \frac{x (e^{5 x} - 1)}{\ln (\frac{x}{- 2 - \ln (\ln (x) - x)})}$

command

int((((((1+5*x)*exp(5*x)-1)*ln(x)+(-5*x^2-x)*exp(5*x)+x)*ln(ln(x)-x)+((10*x+2)*exp(5*x)-2)*ln(x)+(-10*x^2-2*x)*exp(5*x)+2*x)*ln(-x/(ln(ln(x)-x)+2))+((-exp(5*x)+1)*ln(x)+x*exp(5*x)-x)*ln(ln(x)-x)+(-2*exp(5*x)+2)*ln(x)+(x+1)*exp(5*x)-x-1)/((ln(x)-x)*ln(ln(x)-x)+2*ln(x)-2*x)/ln(-x/(ln(ln(x)-x)+2))^2,x)

Maple 2022.1 output

$\int \frac{((((1 + 5 x) e^{5 x} - 1) \ln (x) + (- 5 x^{2} - x) e^{5 x} + x) \ln (\ln (x) - x) + ((10 x + 2) e^{5 x} - 2) \ln (x) + (- 10 x^{2} - 2 x) e^{5 x} + 2 x) \ln (- \frac{x}{\ln (\ln (x) - x) + 2}) + ((- e^{5 x} + 1) \ln (x) + x e^{5 x} - x) \ln (\ln (x) - x) + (- 2 e^{5 x} + 2) \ln (x) + (x + 1) e^{5 x} - x - 1}{((\ln (x) - x) \ln (\ln (x) - x) + 2 \ln (x) - 2 x) \ln {(- \frac{x}{\ln (\ln (x) - x) + 2})}^{2}} d x$

Maple 2021.1 output


method	result	size

risch	$- \frac{2 i x (e^{5 x} - 1)}{π csgn (\frac{i}{\ln (\ln (x) - x) + 2}) csgn {(\frac{i x}{\ln (\ln (x) - x) + 2})}^{2} - π csgn (\frac{i}{\ln (\ln (x) - x) + 2}) csgn (\frac{i x}{\ln (\ln (x) - x) + 2}) csgn (i x) + π csgn {(\frac{i x}{\ln (\ln (x) - x) + 2})}^{3} - 2 π csgn {(\frac{i x}{\ln (\ln (x) - x) + 2})}^{2} + π csgn {(\frac{i x}{\ln (\ln (x) - x) + 2})}^{2} csgn (i x) + 2 π - 2 i \ln (x) + 2 i \ln (\ln (\ln (x) - x) + 2)}$	$175$

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