Q.12 Evaluate : ∫ fracdxx + x⁻¹⁰

Answer: 1/11log|x¹¹ + 1| + c frac1x + x⁻¹⁰ = fracx¹⁰x¹¹ + 1 . Put x¹¹ + 1 = t , so 11x¹⁰ dx = dt . I = ∫ fracx¹⁰x¹¹ + 1dx = 1/11∫ dt/t = 1/11log|t| + c = 1/11log|x¹¹ + 1| + c .

Evaluate : \(\int \frac{dx}{x + x^{-10}}\)

Q.12 Evaluate : \(\int \frac{dx}{x + x^{-10}}\)

Doubtly Asked 28 Oct 2026 Board exam · July 2025 hsc 12th Save WhatsApp Report

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Answer: \(\frac{1}{11}\log|x^{11} + 1| + c\)

\(\frac{1}{x + x^{-10}} = \frac{x^{10}}{x^{11} + 1}\). Put \(x^{11} + 1 = t\), so \(11x^{10}\,dx = dt\).

\(I = \int \frac{x^{10}}{x^{11} + 1}dx = \frac{1}{11}\int \frac{dt}{t} = \frac{1}{11}\log|t| + c = \frac{1}{11}\log|x^{11} + 1| + c\).

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report

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Evaluate : \(\int \frac{dx}{x + x^{-10}}\)

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