Indefinite Integration

Find:

    \[\int xe^{x}\,\mathrm{d}x\]

Sources:

  • Anton, H. (1984). Calculus with Analytic Geometry (2nd ed.). New York: John Wiley & Sons. (Example 1, p. 476-477)
  • Burghes, D., Cassell, D., Cross, T., Deft, J., Middle, J., & Thallon, W. (1994). Pure Mathematics. Oxford, England: Heinemann Educational Books. (Example, p. 363)
  • Gilbert, J. (1991). Guide to Mathematical Methods. Hampshire, England: Macmillan. (Examples 3.7.1: Question 1, p. 63)
  • Taylor, A.E. (1959). Calculus with Analytic Geometry (Volume Two). New York: Ishi Press. (Exercise 10.5, Question 1(a), p. 348)
  • Thompson, S.P. (1946). Calculus Made Easy (3rd ed.). New York: St. Martin’s Press. (Example 2, p. 189)

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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