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The value of the definite integral $\int_{1}^{e}\sqrt{x}\ln(x)dx$ is

  1. $\dfrac{4}{9}\sqrt{e^3}+\dfrac{2}{9} \\$
  2. $\dfrac{2}{9}\sqrt{e^3}-\dfrac{4}{9} \\$
  3. $\dfrac{2}{9}\sqrt{e^3}+\dfrac{4}{9}\\$
  4. $\dfrac{4}{9}\sqrt{e^3}-\dfrac{2}{9}$
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