# Revision history [back]

Thanks for reporting, this is clrealy a bug, it is now trac ticket 30353. The latest Maxima release fixes it, so, when trac ticket 30063 will be merged, you will get:

sage: a = var('a')
sage: assume(a>0)
sage: assume(a<1)
sage: f = integrate(x*log(1/(a*x+(1-x)^2)), x, 0, 1)
sage: f
1/4*a^2*log(a) + 1/2*sqrt(-a^2 + 4*a)*a*arctan(sqrt(-a^2 + 4*a)*(a - 2)/(a^2 - 4*a)) - 1/2*sqrt(-a^2 + 4*a)*a*arctan(sqrt(-a^2 + 4*a)/(a - 4)) - a*log(a) - sqrt(-a^2 + 4*a)*arctan(sqrt(-a^2 + 4*a)*(a - 2)/(a^2 - 4*a)) + sqrt(-a^2 + 4*a)*arctan(sqrt(-a^2 + 4*a)/(a - 4)) - 1/2*a + 3/2
sage: f = integrate(x*log(1/(a*x+(1-x)*(1-x))), x, 0, 1, algorithm='sympy')
sage: f.simplify_full()
1/4*(a^2 - 4*a + 2)*log(1/2*a + 1/2*sqrt(a^2 - 4*a)) - 1/4*(a^2 - 4*a + 2)*log(1/2*a + 1/2*sqrt(a^2 - 4*a) - 1) + 1/4*(a^2 - 4*a + 2)*log(1/2*a - 1/2*sqrt(a^2 - 4*a)) - 1/4*(a^2 - 4*a + 2)*log(1/2*a - 1/2*sqrt(a^2 - 4*a) - 1) + 1/4*sqrt(a^2 - 4*a)*((a - 2)*log(1/2*a + 1/2*sqrt(a^2 - 4*a)) - (a - 2)*log(1/2*a + 1/2*sqrt(a^2 - 4*a) - 1) - (a - 2)*log(1/2*a - 1/2*sqrt(a^2 - 4*a)) + (a - 2)*log(1/2*a - 1/2*sqrt(a^2 - 4*a) - 1)) - 1/2*a - 1/2*log(a) + 3/2
sage: f.limit(a=0)
-I*pi + 3/2