Reduction Formula

Derive the reduction formula below:

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

Source:

Edwards, C.H., & Penney, D.E. (1986). Calculus and Analytic Geometry (2nd ed.). Englewood Cliffs, NJ: Prentice-Hall. (Example 6, p. 467)

Porter, R.I. (1963). Further Elementary Analysis (2nd ed.). London: G. Bell & Sons. (Example 12, p. 234)

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.

Leave a Reply