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