The value of the definite integral \int ↙\stackrel{e}{1}⁡\sqrt{x}\ln ⁡ (x) dx is

\frac{4}{9}\sqrt{e^{3} + \frac{2}{9}

\frac{2}{9}\sqrt{e^{3}−\frac{4}{9}

\frac{2}{9}\sqrt{e^{3} + \frac{4}{9}

\frac{4}{9}\sqrt{e^{3}−\frac{2}{9}

GATE Mechanical Engineering (ME) 2013 Solved Paper

Question : 57 of 65

Marks: +1, -0

The value of the definite integral

∫ ↙{1}↖{e}⁡{√{x}}\ln ⁡ (x) dx

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