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Question
Find `int (x + 1)/((x + 2)(x + 3)) dx`.
Sum
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Solution
`int (x + 1)/((x + 2)(x + 3)) dx = int (x + 2 - 1)/((x + 2)(x + 3)) dx`
⇒ `int (x + 1)/((x + 2)(x + 3)) dx = int 1/((x + 3)) dx - int {1/((x + 2)) - 1/((x + 3))} dx`
= log |x + 3| – log |x + 2| + log |x + 3| + C
⇒ `int (x + 1)/((x + 2)(x + 3)) dx = 2 log |x + 3| - log |x + 2| + "C"`
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