Question

∫ ( cos^4(3x)) d x ​

Answer 1

⅜ x + ¹/₁₂ sin(6x) + ¹/₉₆ sin(12x) + C

Explanation:

∫ cos⁴(3x) dx

Use power reduction formula:

⅛ ∫ (3 + 4cos(6x) + cos(12x)) dx

⅜ ∫ dx + ½ ∫ cos(6x) dx + ⅛ ∫ cos(12x) dx

⅜ ∫ dx + ¹/₁₂ ∫ 6 cos(6x) dx + ¹/₉₆ ∫ 12 cos(12x) dx

⅜ x + ¹/₁₂ sin(6x) + ¹/₉₆ sin(12x) + C