Question

If \( \displaystyle \int \frac{dx}{(x+2)(x^2+1)} = p\log|x+2| + q\log|x^2+1| + r\tan^{-1}x + c \), then \( p+q+r = \)

• A. \( \frac{2}{5} \)
• B. \( \frac{1}{2} \)
• C. \( \frac{7}{10} \)
• D. 16

Hint:

For rational functions with linear and quadratic factors, use partial fractions before integration.

Answer 1

The Correct Option is B