Vault Of Euclid

Evaluating an Improper Integral with a Logarithm

Integrals core

Evaluate \( \int_e^\infty \frac{dx}{x \ln x \sqrt{\ln x}} \).
improper-integralintegration-by-substitutionnatural-logarithmlimit-at-infinitypower-ruleevaluate-integralcalculus-iiconvergence

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What you need first

What this problem tests

Tests the ability to recognize an improper integral, apply substitution correctly, and evaluate a limit at infinity.

This problem is typical of a Calculus II course when introducing improper integrals and reviewing integration techniques.

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