Question

Integration of (Sin(x) + Cos(x))e^x is?

(a) e^x Cos(x)

(b) e^x Sin(x)

(c) e^x Tan(x)

(d) e^x (Sin(x) + Cos(x))

I had been asked this question by my college professor while I was bunking the class.

Question is taken from Improper Integrals in section Integral Calculus of Engineering Mathematics

Answer 1

The correct choice is (b) e^x Sin(x)

Easiest explanation: Add constant automatically

Let f(x) = e^x Sin(x)

∫e^x Sin(x)dx = e^x Sin(x) – ∫e^x Cos(x)dx

∫e^x Sin(x)dx + ∫e^x Cos(x)dx = ∫e^x [Cos(x) + Sin(x)]dx = e^x Sin(x).