Question

The integral \( \int e^x \left(\tan^{-1}x + \frac{1}{1+x^2}\right) dx \) is equal to

• A. \( e^x (\tan^{-1}x + 2) + C \)
• B. \( \tan^{-1}x + C \)
• C. \( e^x \tan^{-1}x + C \)
• D. \( e^x \cot^{-1}x + C \)

Hint:

Always look for the pattern \( \int e^x (f(x) + f'(x)) dx \) when you see an \( e^x \) multiplied by a sum of functions. Identifying \( f(x) \) and its derivative \( f'(x) \) simplifies the integral significantly.

Answer 1

The Correct Option is C