TheAntiderivativeVanishingAtZeroOverAPowerOfALinear​(AngouriMath.​Entity,​AngouriMath.​Entity.​Variable)

N = x M is read off N' (s + t x) - (q - 1) t N = P coefficient by
coefficient: (j + 1) s n_(j + 1) = p_j + (q - 1 - j) t n_j from n_0 = 0,
which is the constant that makes it vanish at zero, and the equation at
x^(q - 1) is p_(q - 1) = 0, the degree bound, which says that there is
no logarithm in it. Each coefficient is put in lowest terms over the symbols as it is
made, so that those of the lower powers that are zero are written as zero: for
x^5/(d + k x)^7 only n_6 = 1/(6 d) is not, and the antiderivative is
x^6/(6 d (d + k x)^6), where the integral of the rational function, matched to
the pole, was six powers of the linear and a constant.