Indefinite Integral

Find the following integral:

    \[\int x^{2}e^{-x}\,\mathrm{d}x\]

Answer:

    \[-e^{-x}\left(x^{2}+2x+2\right)+C\]

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 (xxxxv))

(2) Spiegel, M.R. (1983). Schaum’s Outline of Theory and Problems of Advanced Mathematics for Engineers and Scientists (adapted for SI units by A.N. Pettitt). New York: McGraw-Hill. (Question 1.98(e), p. 32)

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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