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Question
Find `int x/(x^2 + 3x + 2) dx`
Sum
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Solution
`int (xdx)/(x^2 + 3x + 2) = 1/2 int (2x + 3)/(x^2 + 3x + 2) - 3/2 int dx/(x^2 + 3x + 2)`
= `1/2 log |x^2 + 3x + 2| - 3/2 int dx/((x + 3/2)^2 - (1/2)^2)`
= `1/2 log |x^2 + 3x + 2| - 3/2 xx 1/(2 xx 1/2) log |(x + 3/2 - 1/2)/(x + 3/2 + 1/2)| + C`
⇒ `int (xdx)/(x^2 + 3x + 2) = 1/2 log |x^2 + 3x + 2| - 3/2 log |(x + 1)/(x + 2)| + C`
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