Question

Evaluate the indefinite integral: \[ \int e^x (\sin x + \cos x)\, dx \]

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

Hint:

Whenever you see \(e^x\) multiplied by a sum of two functions, check if one is the derivative of the other. It often indicates a direct \(e^x[f(x)+f'(x)]\) pattern.

Answer 1

The Correct Option is B