Indefinite Integration

Prove that \displaystyle \int \frac{1}{a-x}\,\textrm{d}x may lead to either of the expressions \displaystyle \ln{\frac{1}{a-x}} or \displaystyle \ln{\frac{1}{x-a}} and explain how the two solutions may be reconciled.  Find the value of \displaystyle \int_{2}^{4} \frac{1}{1-x^{2}}\,\textrm{d}x.

Source: Porter, R.I. (1963). Further Elementary Analysis (2nd ed.). London: G. Bell & Sons. (Miscellaneous Examples, Question 17, p. 222)

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