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Integrate the follwing functions: (2x)/(...

Integrate the follwing functions: `(2x)/(x^2+3x+2)`

Text Solution

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Let `(2x)/(x^2+3x+2) = (2x)/((x+1)(x+2)) = A/(x+1) + B/(x+2)`
Then 2x = A(x+2)+b(x+1)....(a)
Putting x = -1 and x = -2 in (a)
we have -2 = `Axx1 gtA = -2`,
-4 = `Bxx-1 gt B = 4`
therefore `int (2x)/(x^2+3x+2) dx`
= `-2log|x+1|+4 log|x+2|+c`
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