AP EAMCET · Maths · Indefinite Integration
\(\int \frac{2}{1+x+x^2} d x=\)
- A \(\frac{4}{\sqrt{3}} \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)+c\)
- B \(\frac{4}{\sqrt{3}} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+c\)
- C \(\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)+c\)
- D \(\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+c\)
Answer & Solution
Correct Answer
(B) \(\frac{4}{\sqrt{3}} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+c\)
Step-by-step Solution
Detailed explanation
\(I=\int \frac{2}{1+x+x^2} d x=\int \frac{2}{\left(x+\frac{1}{2}\right)^2+\frac{3}{4}} d x\) Let \(x+\frac{1}{2}=v \Rightarrow d x=d v\)…
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