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Question
Evaluate the following : `int (1)/(x^2 + 8x + 12).dx`
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Solution
`int (1)/(x^2 + 8x + 12).dx`
= `int (1)/((x^2 + 8x + 16) - 16 + 12).dx`
= `int (1)/((x + 4)^2 - 2^2).dx`
= `(1)/(2(2)) log |((x + 4) - 2)/((x + 4) + 2)| + c`
= `(1)/(4) log |(x + 2)/(x + 6)| + c`.
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