By completing the square: . Thatcannotbe factored in terms of real numbers and so you cannot use "partial fractions". Make the substitution u= x+ 1/2 instead.

Here, completing the square gives .and this

(1/sqrt(2)*x+1)dx/(x^2-x*sqrt(2) +1)

Again, youcan'tuse partial fractions. Make the substitution instead.