Evaluate the integral without using tables.

${\int}_{0}^{1}x\mathrm{ln}xdx$

sibuzwaW
2021-11-07
Answered

Evaluate the integral without using tables.

${\int}_{0}^{1}x\mathrm{ln}xdx$

You can still ask an expert for help

Willie

Answered 2021-11-08
Author has **95** answers

Evaluate the integrals as follows:

Substitute$u=\mathrm{ln}x,du=\frac{1}{x}dx,{v}^{\prime}=x,v=\frac{{x}^{2}}{2}\text{}\in \text{}\int udv=uv-\int vdu$ .

$\int}_{0}^{1}x\mathrm{ln}\left(x\right)dx={[\frac{1}{2}{x}^{2}\mathrm{ln}\left(x\right)-\int \frac{x}{2}dx]}_{0}^{1$

$={[\frac{1}{2}{x}^{2}\mathrm{ln}\left(x\right)-\frac{{x}^{2}}{4}]}_{0}^{1}$

$=-\frac{1}{4}$

Substitute

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