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How to integrate this?

x^2 /(1+ 2*x^2 + x^4)

I have no idea how to start it.

Cheers

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Reply 1
Original post by zactissue
x^2 /(1+ 2*x^2 + x^4)

I have no idea how to start it.

Cheers

Posted from TSR Mobile


Hmmmmm I would factorise the denominator giving (x1+x2)2(\frac{x}{1+x^2})^2 to start with
(edited 10 years ago)
Reply 2
Original post by TenOfThem
Hmmmmm I would factorise the denominator giving (x1+x)2(\frac{x}{1+x})^2 to start with


Should be 1+x^2 on the bottom, not 1+x.
Reply 3
Original post by james22
Should be 1+x^2 on the bottom, not 1+x.


yep
Reply 4
You need to use partial fractions for this, start of splitting it into the simplest partial fractions you can then integrate term by term (still not simple though). You will need to use 2 trig substitutions.
Reply 5
Original post by james22
You need to use partial fractions for this, start of splitting it into the simplest partial fractions you can then integrate term by term (still not simple though). You will need to use 2 trig substitutions.

It can be done with one substitution, without splitting up the fraction.
Original post by notnek
It can be done with one substitution, without splitting up the fraction.

Indeed.

x=tanux=\tan u, OP.
Reply 7
Original post by notnek
It can be done with one substitution, without splitting up the fraction.


Good point.

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