Definite Integration

Prove that:

    \[\int_{0}^{\frac{\pi}{4}} \frac{1}{9\cos^{2}{x}-\sin^{2}{x}}\,\textrm{d}x=\frac{1}{6}\ln{2}\]

Source: Porter, R.I. (1963). Further Elementary Analysis (2nd ed.). London: G. Bell & Sons. (Chapter II Miscellaneous Examples, Question 27(ii), p. 35)

Author: ascklee

Dr. Lee teaches at the Wee Kim Wee School of Communication and Information at the Nanyang Technological University in Singapore. He founded The Mathematics Digital Library in 2013.

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