I'm betting I have to solve it using partial fractions : . So I found , , and and I reached to that the solution must be equal to . And I'm stuck here! This last integral looks quite simple I know, and is very similar to , but I don't know how to solve it. I tried by integration by parts, u-substitution. Should I try for trigonometric substitution? If yes, please start me up making a good choice for the sub. I'm not used to trigo-sub... Thanks.
Your answer interests me!
But I just realized I just showed a formula that fit exactly with this integral! Look at one of my earlier post...
So the integral equals to . Thus the final result follows.
But as I said, I'd like you to help me more about this trig-sub.