SOLUTION: Please help me Evaluate this indefinite integral! <img src="https://image.prntscr.com/image/y3fr5X9lQEK3cqDHbP_jhg.png"> Also, I would like to know if I can use the sum/differen

Question 1085429: Please help me Evaluate this indefinite integral!

Also, I would like to know if I can use the sum/difference rule. like this

or only decomposition works

Note: I got difference answers for both but, I don't even know if am allow to use the sum/difference rule on this Integral.
Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
integral (-x^2 + 3 x + 4)/(x (x + 2)^2) dx =
integral (-2/(x + 2) + 3/(x + 2)^2 + 1/x) dx =
-2 integral 1/(x + 2) dx + 3 integral 1/(x + 2)^2 dx + integral 1/x dx
-2 integral 1/u du + 3 integral 1/(x + 2)^2 dx + integral 1/x dx
-2 log(u) + 3 integral 1/(x + 2)^2 dx + integral 1/x dx
-2 log(u) + 3 integral 1/s^2 ds + integral 1/x dx
-3/s - 2 log(u) + integral 1/x dx
-3/s - 2 log(u) + log(x) + constant
((x + 2) (log(x) - 2 log(u)) - 3)/(x + 2) + constant
((x + 2) (log(x) - 2 log(x + 2)) - 3)/(x + 2) + constant
= (-3/(x + 2)) + log(x) - 2 log(x + 2) + constant
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