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