Q.2 (iii) Evaluate : displaystyle∫ 2x/1 + x²dx

Answer: log|1 + x²| + c The numerator 2x is the derivative of the denominator 1 + x² , and displaystyle∫f'(x)/f(x)dx = log|f(x)| + c .

Evaluate : \(\displaystyle\int \frac{2x}{1 + x^2}dx\)

Q.2 (iii) Evaluate : \(\displaystyle\int \frac{2x}{1 + x^2}dx\)

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

Best answer

Answer: \(\log|1 + x^2| + c\)

The numerator \(2x\) is the derivative of the denominator \(1 + x^2\), and \(\displaystyle\int\frac{f'(x)}{f(x)}dx = \log|f(x)| + c\).

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

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