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Example 1 Determine whether the improper integral converges or diverges.

Example 1 Determine whether the improper integral converges or diverges. Solution Since ln x  x ln x for x  3, it follows that for x  3. In Example 4.9.7 (5), we showed the improper integral diverges.

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Example 1 Determine whether the improper integral converges or diverges.

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  1. Example 1 Determine whether the improper integral converges or diverges. Solution Since ln x  xln x for x  3, it follows that for x  3. In Example 4.9.7 (5), we showed the improper integral diverges. By the Comparison Test, the larger improper integral must also diverge.

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