Part 5

[Dimm_summ]

Is it just me or are these questions harder than the rest?  I can't seem to get a single one...  any tips would be greatful...

[BlingBling]

They are a little hard but if you go through and try different techniques then you should eventually get them, they often require a couple different techniques from chapter 8.  However, I'll give you a few hints on the ones I've done so far:
(i)rewrite as 1/(Sqrt(2-x^2))^3 then apply one of the trig substitutions from 8.4
(ii) complete the sqaure of the quadratic in the denominator then apply one of the trig substitutions from 8.4
(iii) apply one of the rationalizing substitutions from 8.6 then divide the resulting rational function to get a binomial plus 1 over a quadratic approach this 1/quadratic part similarily to part ii
(iv) apply one of the rationalizing substitutions from 8.6 then split it up into partial fractions as in 8.5
(v) use the formula for difference of cubes then split it up into partial fractions as in 8.5
(vi) apply one of the trig substitutions from 8.4 and it reduces to S((secu)^3)du and it tells how to do this in the book in 8.3 I believe.
That's all I've done so far.  Chances are my techniques are somewhat faulty and my explainations are confusing but I tried my best, hopefully this will help a little.

[Fire Flower]

Actually I didn't use partial fractions for IV but still got a really slick answer (2 arctan rt(e^x-1) + C
first do a u substitution for e^x-1 then another sub to get rid of the sqrt  (maybe you could do that in one step but by breaking it up I don't squrew up)
You should end up with the arctan derivative.  

QUESTION!!!!
how do you take the integral for
           1              
x² + x + 1

[Fire Flower]

Never mind.

I just found my notes on completing the square.
All is well with the world  8).

[Polska]

God these are dirty.  Its taking me forever to do them.

[Brutal_Chicken]

Anyone have a clue as to how to do x? I substituted x = 2tanu and x³ = 8tan³u dx = 2sec²u.

I got stuck for S tanu sec³u du.

[Miss_Kranky]

any ideas on v?  I used partial fraction first, but... it then got even messier... *shivers*... any help would be most appreciated!!!

[JebusMeany]

Worst. Problem Set. Ever.

[1.8T]

JebusMeany said:

Worst. Problem Set. Ever.

I AGREE.., questions that i dunno how to do are more than the ones i know how to do.,
right now i skipped, #8 of 8.3, 34 of 8.4, 4, 32, 34 of 8.5 all of 8.6 all of 5
and i'm just gonna hand it in as is.,,.., no point stressing over this.,.,., i mean if u mess up 1 question on a test or exam its prob worth more than all the psets put together.,., ,,
but then again., if they put questions like this on the test.,., ..., well  lets just hope they don't.,,.  

[Observer]

I'm currently in the exactly the same situation as you 1.8T except I managed to get 34 from 8.4 done somehow. I've yet to start part 5 because 8.5 and 8.6 are giving me problems!

[1.8T]

actually i got 34 just now.,
b4 i did it the book's way., with the tan and stuff.,
then i get
tanxsecx.,,. and didn't know how to solve
so i just did the u-sub method.,., and got the answer.,., i'm sure we're not suppose to do it this way though., hahahaha