How do you integrate $\frac{x^{2} + 2 x - 5}{(x - 2) \cdot (x + 1) \cdot (x^{2} + 1)}$ $(x^2 + 2x -5) / [(x - 2)(x+1)(x^2+1)]$ ?

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How do you integrate $\frac{x^{2} + 2 x - 5}{(x - 2) \cdot (x + 1) \cdot (x^{2} + 1)}$ $(x^2 + 2x -5) / [(x - 2)(x+1)(x^2+1)]$ ?

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Answer 1 · 2016-10-07T04:55:02

$\frac{1}{5} ln | x - 2 | + ln | x + 1 | + \frac{8}{5} a r c tan x - \frac{3}{5} ln ∣ ∣ x^{2} + 1 ∣ ∣ + C$ $1/5 ln |x - 2| + ln |x+1| + 8/5 arc tan x - 3/5 ln |x^2 + 1| + C$

Explanation:

I am not 100% sure for this one but I have attached a picture so that you may see what I did.
Please, feel free to ask any questions and even more, to correct what I did wrong :)
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How do you integrate $\frac{x^{2} + 2 x - 5}{(x - 2) \cdot (x + 1) \cdot (x^{2} + 1)}$ $(x^2 + 2x -5) / [(x - 2)(x+1)(x^2+1)]$ ?

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How do you integrate x2+2x−5(x−2)⋅(x+1)⋅(x2+1)(x^2 + 2x -5) / [(x - 2)*(x+1)*(x^2+1)]?

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How do you integrate $\frac{x^{2} + 2 x - 5}{(x - 2) \cdot (x + 1) \cdot (x^{2} + 1)}$ $(x^2 + 2x -5) / [(x - 2)(x+1)(x^2+1)]$ ?