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

[executioner_c]

 

[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.

 

[J77]

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

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

 

[fourier jr]

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

 

[J77]

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

Care to show us the way...

 

[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.

 

[HallsofIvy]

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.

 

[executioner_c]

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