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AP EAMCET · Maths · Indefinite Integration

\(\int \frac{d x}{x\left(x^4+1\right)}=\)

  1. A \(\log \left(\frac{x}{x^4+1}\right)+c\)
  2. B \(\frac{3}{4} \log \left(x^4+1\right)+c\)
  3. C \(\frac{1}{3} \log \left(\frac{x^3}{x^4+1}\right)+c\)
  4. D \(\frac{1}{4} \log \left(\frac{x^4}{x^4+1}\right)+c\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{1}{4} \log \left(\frac{x^4}{x^4+1}\right)+c\)

Step-by-step Solution

Detailed explanation

\(\mathrm{I}=\int \frac{d x \times x^3}{x\left(x^4+1\right) \times x^3} \Rightarrow \mathrm{I}=\int \frac{x^3 d x}{x^4\left(x^4+1\right)} d x\)…