Indefinite Integral

Find the following integral:

    \[\int \tan^{4} {x} \, \mathrm{d}x\]

Answer:

    \[x-\tan{x}+\frac{1}{3}\tan^{3}{x}+C\]

where C is an arbitrary constant.

Sources:

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

(2) 1970 Higher School Certificate, Paper 2, Question 4(a)

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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