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TS EAMCET · Maths · Indefinite Integration

If \(\int \frac{x+5}{x^2+4 x+5} d x=a \log \left(x^2+4 x+5\right)\) \(+b \tan ^{-1}(x+k)+C\), then \((a, b, k)\) equals

  1. A \(\left(\frac{1}{2}, 3,2\right)\)
  2. B \(\left(\frac{1}{2}, 1,2\right)\)
  3. C \(\left(\frac{1}{2}, 3,1\right)\)
  4. D \((1,3,2)\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\left(\frac{1}{2}, 3,2\right)\)

Step-by-step Solution

Detailed explanation

Let \(I=\int \frac{x+5}{x^2+4 x+5} d x\) Put \(x+5=\lambda(2 x+4)+\mu\) On comparing both sides, we get…