The integral e7𝜃 sin(10𝜃) d𝜃 can be best matched by formula number

I'm sorry, but you didn't provide a specific question or a list of formulas to match the integral with. The integral you provided, ∫e^(7θ) sin(10θ) dθ, is a complex one and would typically require integration by parts or a similar advanced integration technique. If you provide a list of formulas or a more specific question, I'd be happy to help further!