Question

\(\displaystyle \int e^{x}(\cos x-\sin x)\,dx=\) ?

• A. \(e^{x}\sin x+k\)
• B. \(e^{x}\cos x+k\)
• C. \(-e^{x}\sin x+k\)
• D. \(k-e^{x}\cos x\)

Hint:

Look for a known product whose derivative matches the pattern.

Answer 1

The Correct Option is B

Recognize a derivative: \(\dfrac{d}{dx}(e^{x}\cos x)=e^{x}\cos x-e^{x}\sin x=e^{x}(\cos x-\sin x)\). Thus the integral is \(e^{x}\cos x+k\).