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 :)

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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 :)

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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
Ok, thanks anyway. :)
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.

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Wow, this nooby site cut of the last denominator, but hopefully you can see what it is.
Can you explain what you did with the first one? Did you divide or something?
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))
Ok, thank you! That helped me a lot! :)
No problem

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