Q.1 (vii) The value of ∫ x^x(1 + log x) dx is equal to _____. A. 1/2(1 + log x)² + c B. x^2x + c C. x^x·log x + c D. x^x + c

Answer: D. x^x + c Answer: (d) x^x + c Put t = x^x . Then log t = xlog x , so 1/tdt/dx = 1 + log x , i.e. dt = x^x(1 + log x) dx . Hence ∫ dt = t + c = x^x + c .

The value of \(\int x^x(1 + \log x)\,dx\) is equal to _____.

Q.1 (vii) The value of \(\int x^x(1 + \log x)\,dx\) is equal to _____.

A. \(\dfrac12(1 + \log x)^2 + c\)

B. \(x^{2x} + c\)

C. \(x^x\cdot\log x + c\)

D. \(x^x + c\)

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

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Answer: D. \(x^x + c\)

Answer: (d) \(x^x + c\)

Put \(t = x^x\). Then \(\log t = x\log x\), so \(\frac{1}{t}\frac{dt}{dx} = 1 + \log x\), i.e. \(dt = x^x(1 + \log x)\,dx\). Hence \(\int dt = t + c = x^x + c\).

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

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