If ∫ cos x cos 2x cos 5x dx = A<sub>1</sub> sin 2x + A<sub>2</sub> sin 4x + A<sub>3</sub> sin 6x + A<sub>4</sub> sin 8x + c, then the values of A<sub>1</sub>, A<sub>2</sub>, A<sub>3</sub>, A<sub>4</sub> are
(A) <span class="math-tex">\(A_1 = \frac 1 2,\;A_2 = \frac 1 4,\; A_3 = \frac 1 6,\; A_4 = \frac 1 8\)</span>
(B) <span class="math-tex">\(A_1 = \frac 1 8,\;A_2 = \frac 1 {16},\; A_3 = \frac 1 {24},\; A_4 = \frac 1 {32}\)</span>
(C) <span class="math-tex">\(A_1 = \frac 1 6,\;A_2 = \frac 1 {12},\; A_3 = \frac 1 {18},\; A_4 = \frac 1 {24}\)</span>
(D) <span class="math-tex">\(A_1 = \frac 1 4,\;A_2 = \frac 1 8,\; A_3 = \frac 1 {12},\; A_4 = \frac 1 {16}\)</span>