Indefinite Integration

Find:

    \[\int x\sin{x}\,\mathrm{d}x\]

Sources:

Downing, D. (1982). Calculus the Easy Way. New York: Barron’s Educational Series. (Example, p. 134)

Edwards, C.H., & Penney, D.E. (1986). Calculus and Analytic Geometry (2nd ed.). Englewood Cliffs, NJ: Prentice-Hall. (Exercise 9.4: Question 3, p. 468)

Gilbert, J. (1991). Guide to Mathematical Methods. Hampshire, England: Macmillan. (Exercise 3.7.1: Question 1(i), p. 67)

Mathcentre. (2010). Integration by Parts. (Exercises, Question 1(a), p. 7)

Porter, R.I. (1963). Further Elementary Analysis (2nd ed.). London: G. Bell & Sons. (Example 7, p. 230)

Schwartz, A. (1960). Analytic Geometry and Calculus. New York: Holt, Rinehart and Winston. (Exercise 6.6: Question 1, p. 361)

Smyrl, J.L. (1978). An Introduction to University Mathematics. London: Hodder and Stoughton. (Exercise 16(e): Question 1, p. 432)

Taylor, A.E. (1959). Calculus with Analytic Geometry (Volume Two). New York: Ishi Press. (Example 1, p. 347)

Solution:

Use integration by parts.

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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