AP EAMCET · Maths · Indefinite Integration
If \(\int \frac{x^2-x+2}{x^2+x+2} d x=x-\log (f(x))+\frac{2}{\sqrt{7}} \operatorname{Tan}^{-1}(g(x))+c\), then \(\mathrm{f}(-1)+\sqrt{7} \mathrm{~g}(-1)=\)
- A \(1\)
- B \(0\)
- C \(-1\)
- D \(2\)
Answer & Solution
Correct Answer
(A) \(1\)
Step-by-step Solution
Detailed explanation
\( \frac{x^2-x+2}{x^2+x+2} = 1 - \frac{2x}{x^2+x+2} \) \( \int \frac{x^2-x+2}{x^2+x+2} dx = x - \int \frac{2x}{x^2+x+2} dx \) \( \int \frac{2x}{x^2+x+2} dx = \int \frac{(2x+1)-1}{x^2+x+2} dx \) \( = \log(x^2+x+2) - \int \frac{1}{(x+1/2)^2+(\sqrt{7}/2)^2} dx \)…
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