Question

Evaluate the integral \( \int \frac{e^{\tan^{-1} x}}{1 + x^2} \, dx \)

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

Hint:

When evaluating integrals involving \( \tan^{-1} x \), use substitution to simplify the expression.

Answer 1

The Correct Option is B