Final answer:
To integrate ∫ eˣ sin(3x) dx using integration by parts, we need to choose u = sin(3x) and dv = eˣ dx. By finding the respective values of du and v and using the formula for integration by parts, we can simplify the expression and evaluate the integral.
Step-by-step explanation:
To integrate the expression ∫ eˣ sin(3x) dx using the method of integration by parts, we will choose u = sin(3x) and dv = eˣ dx. From this, we can find du and v by differentiating and integrating, respectively. Then, we use the formula for integration by parts, which states that ∫ u dv = uv - ∫ v du. Plugging in the values we found, we can simplify the expression and evaluate the integral.