Question

Evaluate the integral: \(\int \frac{2x}{x^2 - 5x + 4} \, dx\)

• A. \( \frac{8}{3}\log |x-4| - \frac{2}{3}\log |x-1| + C \)
• B. \( \frac{2}{3}\log |x-4| - \frac{8}{3}\log |x-1| + C \)
• C. \( \frac{8}{3}\log |x-1| - \frac{2}{3}\log |x-4| + C \)
• D. \( \frac{2}{3}\log |x-1| - \frac{8}{3}\log |x-4| + C \)

Hint:

For partial fractions of the form \( \frac{f(x)}{(x-a)(x-b)} \), use the "cover-up" method:
To find \( A \), cover \( (x-4) \) and put \( x=4 \) in the rest of the expression: \( \frac{2(4)}{4-1} = 8/3 \).

Answer 1

The Correct Option is A