3) Evaluate the following integrals i). /²(6+3 cos x) dx ii). (1-e-²x) dx iii). ₂(1-x-4x³ + 2x5) dx a) Analytically b) Single application of the trapezoidal rule c) Multiple-application trapezoidal rule with n = 2 & 4

1 dx ½ x* -1 1 a) arctan -In 3+ 3 4 8 1 b) -arctan 3 --In 2+ 3 4 8 c) -arctan 3 +-In2+ 4 8 1 1 arctan-+-In 3 3 4 8

(1) S(1+x² ) (2 – x) dx (2) S Vx? .- S VIZ - + 4 dx x5 +2x² -1 3) x4 xp (4) S" 5 e* + 3 sinx dx (5) SF sinx + sinx tan² x sec² x xp