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
- A \(\left(\frac{1}{2}, 3,2\right)\)
- B \(\left(\frac{1}{2}, 1,2\right)\)
- C \(\left(\frac{1}{2}, 3,1\right)\)
- D \((1,3,2)\)
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…
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