Indefinite Integral

Find the following integral:

    \[\int \frac{x^{3}+1}{x \left( x^{3}+4 \right)} \, \mathrm{d}x\]

Answer:

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

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 (xxv))

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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