Question

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 :)

Answer 1

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

Answer 2

Ok, thanks anyway. :)

Answer 3

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.

Answer 4

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

Answer 5

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

Answer 6

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))

Answer 7

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

Answer 8

No problem