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

Answer: e^x/x The integrand is of the form e^x[f(x)+f'(x)] with f(x)=1/x , f'(x)=-1/x² . Hence the integral is e^xf(x)+c=e^x/x+c .

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

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

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

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

The integrand is of the form \(e^x[f(x)+f'(x)]\) with \(f(x)=\frac{1}{x}\), \(f'(x)=-\frac{1}{x^2}\). Hence the integral is \(e^xf(x)+c=\frac{e^x}{x}+c\).

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

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

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