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TS EAMCET · Maths · Indefinite Integration

\(\int \frac{x^5+x}{x^8+1} d x=\)

  1. A \(\frac{1}{2 \sqrt{2}} \tan ^{-1}\left(\frac{x^4-1}{\sqrt{2} x^2}\right)+c\)
  2. B \(\log \left(x^5+x^2\right)-\log \left(x^3+x\right)+\log (x+1)+c\)
  3. C \(\frac{2}{9} x^8-\frac{4}{9} x^6+\frac{1}{9} x^4-\frac{1}{3} x^2+c\)
  4. D \(\frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{x^5-1}{\sqrt{2} x^3}\right)+c\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{1}{2 \sqrt{2}} \tan ^{-1}\left(\frac{x^4-1}{\sqrt{2} x^2}\right)+c\)

Step-by-step Solution

Detailed explanation

Let \(x^2=8 \Rightarrow 2 x d x=d t\)…