AP EAMCET · Maths · Indefinite Integration
If \(\int \frac{x^2+1}{x^4+1} d x=f(x)+c\), then \(f(x)\) is equal to
- A \(\frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{x^2+1}{\sqrt{2} x}\right)\)
- B \(\frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{x^2-1}{\sqrt{2} x}\right)\)
- C \(\frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{1-x^2}{\sqrt{2} x}\right)\)
- D \(\frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{1+x^4}{\sqrt{2} x}\right)\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{x^2-1}{\sqrt{2} x}\right)\)
Step-by-step Solution
Detailed explanation
\(\int \frac{x^2+1}{x^4+1} d x=f(x)+c\) Let…
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