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