Mathematics · JEE | INTEGRALS

What is the value of \( \int \frac{x^2 + 1}{(x-2)(x-3)} dx \) when expressed in terms of polynomials and logarithmic components?

1. A
   \( x + 5 \log |x-2| - 10 \log |x-3| + C \)
2. B
   \( x - 5 \log |x-2| + 10 \log |x-3| + C \)
3. C
   \( x - 10 \log |x-2| + 5 \log |x-3| + C \)
4. D
   \( 1 - 5 \log |x-2| + 10 \log |x-3| + C \)