Evaluate ∫(√(x²+1) [ln(x²+1) − 2ln x])/x⁴ dx. A. Complex integration, cannot be solved B. Requires trigonometric substitution C. Solved by substituting u = 1 + 1/x² D. Solved by partial fractions Answer: C) Solved by substituting u = 1 + 1/x² Explanation: Rewriting integrand. √(x²+1)/x⁴ = (1/x³)√(1+1/x²). ln((x²+1)/x²) = ln(1+1/x²). Substitute u = 1+1/x² simplifies it greatly.

imo class 12 indefinite integration

Evaluate ∫(√(x²+1) [ln(x²+1) − 2ln x])/x⁴ dx.

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Evaluate ∫(√(x²+1) [ln(x²+1) − 2ln x])/x⁴ dx.

Answer: C) Solved by substituting u = 1 + 1/x²

Explanation: Rewriting integrand. √(x²+1)/x⁴ = (1/x³)√(1+1/x²). ln((x²+1)/x²) = ln(1+1/x²). Substitute u = 1+1/x² simplifies it greatly.