## anonymous 5 years ago Integration: Out of the following methods, substitution/ parts/ partial fractions, which methods would you choose to solve each of these integrals? 1) x^2 dx / (x^2+x-2) 2) dx / (x^3+9x) 3) dx / (x^4-a^4) 4) (x^2+1) / (x^3+8) And can you explain why please? Thank you :)

1. anonymous

no, these are too hard for me :( I wish lokisan or sstarica would be logged in, I am sure they would be able to help

2. anonymous

Ok, thanks anyway. :)

3. anonymous

For 1, note $\frac{x^2}{x^2+x-2} = \frac{(x^2+x-2)-(x-2)}{x^2+x-2} = 1-\frac{x-2}{(x+2)(x-1)}$ then split it up into partial fraction (IMO) 2 is a partial fractions jobby. The other two would probably work with partial fractions but (if you're lucky) I'll try and see what is best.

4. anonymous

Wow, this nooby site cut of the last denominator, but hopefully you can see what it is.

5. anonymous

Can you explain what you did with the first one? Did you divide or something?

6. anonymous

It's called 'adding nothing' (or similar); it's essentially a slick version of long division, yes - if the numerator and denominator are of the same order ALWAYS divide. If I don't see anything else, partial fractions should work for the last two: 3 is difference of two squares (twice!), and for the last one it should work too, as long as you see a factor (think what (simple) number will make the denominator = 0))

7. anonymous

Ok, thank you! That helped me a lot! :)

8. anonymous

No problem