Evaluate: ∫ (x² - 1) / (x⁴ + 1) dx A. (1/(2√2)) log|(x² - √2 x + 1)/(x² + √2 x + 1)| + C B. 1/2 log|(x²-x+1)/(x²+x+1)| + C C. (1/2) tan⁻¹((x²-1)/(√2 x)) + C D. (1/(2√2)) log|(x² + √2 x + 1)/(x² - √2 x + 1)| + C Answer: A) (1/(2√2)) log|(x² - √2 x + 1)/(x² + √2 x + 1)| + C Explanation: Divide numerator and denominator by x². Substitute t = x + 1/x, giving ∫ dt / (t² - 2). Result is (1/(2√2)) log|(t-√2)/(t+√2)| + C.

imo class 12 indefinite integration

Evaluate: ∫ (x² - 1) / (x⁴ + 1) dx

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Evaluate: ∫ (x² - 1) / (x⁴ + 1) dx

Answer: A) (1/(2√2)) log|(x² - √2 x + 1)/(x² + √2 x + 1)| + C

Explanation: Divide numerator and denominator by x². Substitute t = x + 1/x, giving ∫ dt / (t² - 2). Result is (1/(2√2)) log|(t-√2)/(t+√2)| + C.