Indefinite Integral

Find the following integral:

    \[\int \frac{ 2 \sqrt{2} }{x^{2}+2x-1} \, \mathrm{d}x\]

Answer:

    \[\ln{\left(\frac{x+1-\sqrt{2}}{x+1+\sqrt{2}}\right)}+C\]

where C is an arbitrary constant.

Source: R.L. Rosenberg. (1984). Elementary Calculus: Course Notes. Ottawa, Canada: Holt, Rinehart and Winston. (Additional Exercises in Integration: Question (xxxv))

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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