Q.1 (C) (ii) ∫ e^x(1/x-1/x²)dx = _____.

Answer: e^x/x+c Here f(x)=1/x and f'(x)=-1/x² . Since ∫ e^x[f(x)+f'(x)]dx=e^xf(x)+c , the integral is e^x/x+c .

\(\int e^x\left(\frac{1}{x}-\frac{1}{x^2}\right)dx\) = _____.

Q.1 (C) (ii) \(\int e^x\left(\frac{1}{x}-\frac{1}{x^2}\right)dx\) = _____.

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

Best answer

Answer: \(\frac{e^x}{x}+c\)

Here \(f(x)=\frac{1}{x}\) and \(f'(x)=-\frac{1}{x^2}\). Since \(\int e^x[f(x)+f'(x)]dx=e^xf(x)+c\), the integral is \(\frac{e^x}{x}+c\).

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

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