Question

∫e^x (cos x – sin x)dx is equal to

(A) e^x cos x + C 

(B) e^x sin x + C

(C) – e^x cos x + C

(D) – e^x sin x + C

Answer 1

(A) is the correct answer 

since ∫e^x [ f ( x) + f '( x)] dx = e^x f ( x) + C . Here

f (x) = cosx, f′ (x) = – sin x.