Reduction Formula

Derive the reduction formula below:

    \[\displaystyle \int \tan^{n}{x} \,\mathrm{d}x = \frac{\tan^{n-1}{x}}{n-1} - \int \tan^{n-2} {x} \,\mathrm{d}x\]

Sources:

Edwards, C.H., & Penney, D.E. (1986). Calculus and Analytic Geometry (2nd ed.). Englewood Cliffs, NJ: Prentice-Hall. (p. 462)

Schwartz, A. (1960). Analytic Geometry and Calculus. New York: Holt, Rinehart and Winston. (Exercise 6.7, Question 6, p. 368)

Silverman, R.A. (1985). Calculus with Analytic Geometry. Englewood Cliffs, NJ: Prentice-Hall. (Problems 7.3, Question 26(a), p. 379)

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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