AP EAMCET · Maths · Indefinite Integration
\(\int \frac{x^2-1}{x^3 \sqrt{2 x^4-2 x^2+1}} d x=\)
- A \(\frac{1}{2 \mathrm{x}^2} \sqrt{2 \mathrm{x}^4+2 \mathrm{x}^2+1}+\mathrm{C}\)
- B \(\frac{1}{2 x^2} \sqrt{2 x^4-2 x^2+1}+C\)
- C \(\frac{1}{2 \mathrm{x}^2} \sqrt{4 \mathrm{x}^4-2 \mathrm{x}^2+1}+\mathrm{C}\)
- D \(\frac{1}{2 x^2} \sqrt{4 x^4+2 x^2+1}+C\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{2 x^2} \sqrt{2 x^4-2 x^2+1}+C\)
Step-by-step Solution
Detailed explanation
\(\int \frac{x^2-1}{x^3 \sqrt{2 x^4-2 x^2+1}} d x=\int \frac{\frac{x^2-1}{x^5}}{\frac{x^3 \sqrt{2 x^4-2 x^2+1}}{x^5}} d x\) \(=\int \frac{\frac{1}{x^3}-\frac{1}{x^5}}{\sqrt{2-\frac{2}{x^2}+\frac{1}{x^4}}} d x\) ...(i) Let…
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