COMEDK · Maths · 28. Indefinite Integration
\(\int \dfrac{d x}{(x+2)\left(x^2+1\right)}=p \log |x+2|+q \log \left|x^2+1\right|+r \tan ^{-1} x+c\) then \(p+q+r=\)
- A \(16\)
- B \(\dfrac{2}{5}\)
- C \(\dfrac{1}{2}\)
- D \(\dfrac{7}{10}\)
Answer & Solution
Correct Answer
(C) \(\dfrac{1}{2}\)
Step-by-step Solution
Detailed explanation
Let \(\dfrac{1}{(x+2)(x^2+1)} = \dfrac{A}{x+2} + \dfrac{Bx+C}{x^2+1}\). Multiplying both sides by \((x+2)(x^2+1)\), we get \(1 = A(x^2+1) + (Bx+C)(x+2)\). Setting \(x = -2\), we get \(1 = A(4+1) + 0\), which implies \(5A = 1\), so \(A = \dfrac{1}{5}\). Comparing coefficients of…
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