(a + b x)^(-3)/sqrt(c a + c b x) is integrated on master, from 85d6601c on, as an expression that divides by b a c - a b c, which is 0, so it has no value at any point:
"(a+b*x)^(-3)/sqrt(c*a+c*b*x)".ToEntity().Integrate("x")
(a + b * x) ^ (-2) * (c * a + c * b * x) ^ (1/2) / ((-2) * (b * a * c - a * b * c)) - ...
2.5.0 declines it, and master before #1758 answered it: -2/(5 b) (a + b x)^(-2) (c a + c b x)^(-1/2). Rubi's 1.1.3.2:3412 and 3413, 1/(c (a + b x)^3)^(3/2) and ^(5/2), come to the same.
The recurrence #1758 added, for a negative power of one linear beside a power of another, divides by the two linears' determinant b c' - a d', and declines where that is zero as written. Here it is zero only once the products in it are sorted.
(a + b x)^(-3)/sqrt(c a + c b x)is integrated on master, from85d6601con, as an expression that divides byb a c - a b c, which is 0, so it has no value at any point:2.5.0 declines it, and master before #1758 answered it:
-2/(5 b) (a + b x)^(-2) (c a + c b x)^(-1/2). Rubi's 1.1.3.2:3412 and 3413,1/(c (a + b x)^3)^(3/2)and^(5/2), come to the same.The recurrence #1758 added, for a negative power of one linear beside a power of another, divides by the two linears' determinant
b c' - a d', and declines where that is zero as written. Here it is zero only once the products in it are sorted.