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## Homework Statement

integrate 1/(x+x^3+2)

## Homework Equations

## The Attempt at a Solution

I have tried to use partial fraction but the process is very complicated. Are there any faster methods? It is one of the ten questions in a 50 minutes elementary level test.

Here is my attempt,

∫ 1/(x^3+x+2) dx= ∫ 1/[4(x+1)] dx - ∫ (x-2)/[4(x^2-x+2)] dx

= In(x+1)/4 - ∫ (x-2)/[4((x-1/2)^2+7/4)] dx + C

Then I have to use complicated trigonometry by letting x - 1/2 = (root 7) tan(y) /2

Please tell me if there is a faster method