Primitive of x/sqrt(4+x^4): Is Substitution Necessary?

[esmeco]

I know that tu solve this primitive we have tu use the substitution method,but I think that none of the rules that should be used apply to this!The problem is, to use the substitution: x=a/b sen t we should have the function in the format (sqrt(a^2 - b^2*x^2)),but instead of a x^2 I have a x^4.
I'm studying for an exam about primitives I'm having tomorrow and I really could use some help on this!
Thanks in advance for the reply!

 

[acm]

Let u = x^2
du/dx = 2x
du = 2xdx

Hence 1/2 Integral (1/ Root( u^2 + 4) ) du
Which is a inverse hyperbolic integral.

 

[dextercioby]

Make the substitution x^2 =t.

Daniel.

 

[esmeco]

Now that i look at the primitive,I think it's not necessary to make substitutions...Multyplying the fraction by 1/4 it could be something like: 1/4*x/sqrt(1/4 + (1/4x)^4),which in turn would loook like: 1/4primitive x/sqrt(1/4 + (1/2x^2)2).Since it's no the form f'/sqrt(1-f^2) , the primitive of the function would be: 1/4arcsen(1/2x^2).
Could this be solved this way?
Thanks in advance for the reply!^_^