Indefinite Integral

Find the following integral:

    \[\int \frac{1}{\cos^{2} { \left( \frac{x}{2}  \right)} - \sin^{2} {  \left( \frac{x}{2} \right) }} \, \mathrm{d}x\]

Answer:

    \[\ln{\left[\tan{\left(\frac{1}{4}\pi+\frac{1}{2}x\right)}\right]}+C\]

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 (xxxxi))

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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