CUET · MATHS · PYQ PAPER 2023
If \(\int \frac{2 x}{x^2+3 x+2} d x=m \log |x+2|+n \log |x+1|+C\), then the values of m and n are:
- A \(m=4, n=-2\)
- B \(m=-2, n=4\)
- C \(m=2, n=2\)
- D \(m=6, n=4\)
Answer & Solution
Correct Answer
(A) \(m=4, n=-2\)
Step-by-step Solution
Detailed explanation
\( \frac{2 x}{(x+1)(x+2)} = \frac{A}{x+1} + \frac{B}{x+2} \) \( 2x = A(x+2) + B(x+1) \) \( x=-1 \Rightarrow -2 = A(1) \Rightarrow A=-2 \) \( x=-2 \Rightarrow -4 = B(-1) \Rightarrow B=4 \)…
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