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Definite Integral of a Trigonometric Fraction Yielding a Logarithm

Logarithmic and exponential functions warmup

Evaluate \(\int_{\pi/6}^{\pi/2} \frac{\cos x}{2-\sin x} dx\).
calculus-idefinite-integralevaluate-integralfundamental-theorem-of-calculusintegration-by-substitutionlogarithm-propertiesnatural-logarithmsinecosinetrigonometric-functionsu-substitution

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What this problem tests

Tests the ability to perform u-substitution with trigonometric functions and evaluate definite integrals involving logarithms.

This is a standard Calculus I problem testing the recognition of the f'(x)/f(x) pattern for integration.

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