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Question

Math 6420 • PDE

Fall 1999 • Question 12

Find the leading behavior of the integral \[ I(x)=\int_0^{10}\frac{e^{-xt}}{1+t\log t}\,dt\qquad\text{as }x\to+\infty. \] Explain your rationale.

Raw LaTeX

Find the leading behavior of the integral
\[
  I(x)=\int_0^{10}\frac{e^{-xt}}{1+t\log t}\,dt\qquad\text{as }x\to+\infty.
\]
Explain your rationale.
\end{enumerate}