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

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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. :wink:
 
That's one nasty integral - the Wolfram Integrator gives:

http://img316.imageshack.us/img316/4803/2359mo8.gif

 
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there's a lot there but you still only need standard textbook methods to integrate it.
 
fourier jr said:
there's a lot there but you still only need standard textbook methods to integrate it.
Care to show us the way... :-p
 
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.
 
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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.
 
I've just got the solution.Thanks a lot!
 
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