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integration help

hi guys, im quite stuck with this question. please give me some hints.
integrate[((x^2)-(1/x))^4]

i've tried to let u=the whole thing inside, but unfortunately i don't know how it works.
thanks

Reply 1

$Avatar for Get me off the £\?%!^@ computer$

Get me off the £\?%!^@ computer

I think I'd just multiply it out and then integrate.

Reply 2

kingsclub

by binomial expansion? i thought of that before but i think it would be quite time consuming...

Reply 3

$Avatar for Get me off the £\?%!^@ computer$

Get me off the £\?%!^@ computer

Original post by kingsclub

by binomial expansion? i thought of that before but i think it would be quite time consuming...

It really doesn't take long if you do it instead of thinking about doing it. :wink:

Reply 4

kingsclub

Original post by Get me off the £\?%!^@ computer

It really doesn't take long if you do it instead of thinking about doing it. :wink:

but will it work using the substitution method? cause i want to try that method.

bump

binomial expansion is the best way to go in this case!

Reply 7

Hype en Ecosse

I just did it, all the x^2 and 1/x are different functions, both being in the bracket of the power of four.
The way I thought of it was to say what 1/x is the same as, as a simpler indice, and then applying one of the laws of indices to expand the whole thing.

Alternatively, what might be a better way is use the chain rule. Add one to the power, divide by the (new power times the derivative of the brackets)

Reply 8

ghostwalker

Original post by kingsclub

but will it work using the substitution method? cause i want to try that method.

If you insist on using a substitution.

Put the term in brackets over a common denominator.
Use u=x^3+1 as your substitution.

It would be useful practise as you'll require polynomial division, use of partial fractions, a non-trivial (but not difficult) change of variable, practise on fractional indices, and will probably be challenged to show that it gives the same result (I've only worked it partially through, but it looks doable.).

Have fun!

Reply 9

DFranklin

Original post by mckinnon94

IAlternatively, what might be a better way is use the chain rule. Add one to the power, divide by the (new power times the derivative of the brackets)