The main aim of this research paper is to evaluate a general integral of the form Z 1 0 x d?1 (1 ? x) d+` [1 + ?x + ?(1 ? x)]?2d?`?1 × 4F3 a, b, 2d + ` + 1, c 1 2 (a + b + i + 1), d, 2c + j ; (1 + ?)x 1 + ?x + ?(1 ? x) ...