Indefinite Integration

Prove that  \displaystyle \int \frac{1}{x^{3}+3x^{2}-4}\,\textrm{d}x=\frac{1}{3\left(x+2\right)}+\frac{1}{9}\ln{\frac{x-1}{x+2}}+C.

Source: Porter, R.I. (1963). Further Elementary Analysis (2nd ed.). London: G. Bell & Sons. (Miscellaneous Examples, Question 10, p. 221)

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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