Evaluate eax cos bx dx by modifying the method in part a

Question

Question: Integrating eax sin bx by parts twice gives

∫e^ax sinbx dx = e^ax(A sin bx + B cos bx) + C

(a) Find the constants A and B in terms of a and b. [Hint: Don't actually perform the integration.]

(b) Evaluate ∫ eax cos bx dx by modifying the method in part (a). [Again, do not perform the integration.]