# Evaluate the integral without using tables. \int_{0}^{1}x\ln x dx

sibuzwaW 2021-11-07 Answered
Evaluate the integral without using tables.
${\int }_{0}^{1}x\mathrm{ln}xdx$
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## Expert Answer

Willie
Answered 2021-11-08 Author has 95 answers
Evaluate the integrals as follows:
Substitute .
${\int }_{0}^{1}x\mathrm{ln}\left(x\right)dx={\left[\frac{1}{2}{x}^{2}\mathrm{ln}\left(x\right)-\int \frac{x}{2}dx\right]}_{0}^{1}$
$={\left[\frac{1}{2}{x}^{2}\mathrm{ln}\left(x\right)-\frac{{x}^{2}}{4}\right]}_{0}^{1}$
$=-\frac{1}{4}$
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