# Can anyone kindly show me the steps to solve this question?

1. Sep 7, 2006

2. Sep 7, 2006

### fourier jr

i would start with long division & see what i get. if it turned out to be something that partial fractions would work on i'd do that, or trig substitution etc etc. there's a forum just for homework problems where this thread really belongs.

3. Sep 7, 2006

4. Sep 7, 2006

### fourier jr

there's a lot there but you still only need standard textbook methods to integrate it.

5. Sep 8, 2006

### J77

Care to show us the way... :tongue:

6. Sep 8, 2006

### Robokapp

I'd start by trying to see if either -1 or -4 is a root of the top. That would help you lowert the power of that monstruosity. I doubt it is a non-reductible quintic that you got to integrate...if not, long division, get a rational expression plus a bunch of constant/linear/quadratic parts and integrate it each piece at a time.

If I recall,

$$\int{(a+b)}=\int{a}+\int{b}$$

So all components after the division should be very simple to integrate except the fraction if there is one...and that shouldn't be too bad neither.

Last edited: Sep 8, 2006
7. Sep 8, 2006

### HallsofIvy

Staff Emeritus
As fourierjr said at the beginning: go ahead and do the division. That integrand is equal to
$$x-1- \frac{6x^3+ 6x^2+ 11x+ 1}{(x+1)^2(x^2+ 4)}$$
You can use partial fractions to integrate that fraction.

8. Nov 12, 2006

### executioner_c

I've just got the solution.Thanks a lot!!