Final answer:
To evaluate the integral, use integration by parts method, substitute appropriate values for u and dv, and apply the formula for integration by parts.
Step-by-step explanation:
To evaluate the integral ∫ 4x cos(9x) dx, we can use integration by parts. Let u = 4x and dv = cos(9x) dx. By differentiating u and integrating dv, we can find du and v respectively. Using the formula for integration by parts:
∫ u dv = uv - ∫ v du
∫ 4x cos(9x) dx = 4x * (1/9)sin(9x) - (1/9)∫ sin(9x) dx
Simplifying further: ∫ 4x cos(9x) dx = (4/9)xsin(9x) - (1/81)cos(9x) + C