Q.11 Evaluate: ∫ xlog x dx

Answer: x²/2log x - x²/4 + c Integrating by parts with u = log x , v = x : ∫ xlog x dx = log x·x²/2 - ∫1/x·x²/2 dx = x²/2log x - 1/2∫ x dx = x²/2log x - x²/4 + c .

Evaluate: \(\int x\log x\,dx\)

Q.11 Evaluate: \(\int x\log x\,dx\)

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

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Answer: \(\frac{x^2}{2}\log x - \frac{x^2}{4} + c\)

Integrating by parts with \(u = \log x\), \(v = x\):

\(\int x\log x\,dx = \log x\cdot\frac{x^2}{2} - \int\frac{1}{x}\cdot\frac{x^2}{2}\,dx = \frac{x^2}{2}\log x - \frac{1}{2}\int x\,dx = \frac{x^2}{2}\log x - \frac{x^2}{4} + c\).

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

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Evaluate: \(\int x\log x\,dx\)

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