Question

The value of the integral \[ \int_1^\infty \frac{x+1}{|x-1|} \left( \frac{x-1}{x+1} \right)^{1/2} \, dx \] is

• A. \( \log 3 \)
• B. \( 4 \log 3 \)
• C. \( 4 \log 4 \)
• D. \( \log 4 \)

Hint:

When integrating complex rational functions, use substitution and simplify the integrand before attempting to solve.

Answer 1

The Correct Option is C

Step 1: Simplifying the integral.
This integral is solved by substitution and breaking it down into simpler components. We use standard integration techniques to solve the integral.

Step 2: Conclusion.
The value of the integral is \( 4 \log 4 \), corresponding to option (3).