Question

Integrate ∫ex cos x dx.

Answer 1

I = ∫ex cos x dx

= ex(cos x + exsin x) - ∫cos x ex dx

= ex(cos x + sin x) - ∫ex cos x dx

= ex(cos x + sin x) - I + c

2I = ex(cos x + sin x) + c

I = (1/2)ex (cos x + sin x) + c