# Integral of sqrt(1 + x^4+ 2x^2)

Sidthewall

## Homework Statement

sqrt(1 + x^4+ 2x^2)

## The Attempt at a Solution

k so i need a lead on this one, maybe some kind of substition, i am not quite adept with finding the integrals of a square root function with polynomials in it

ACG
Here's a bit of a hint. When you expand (x+1)^2, what do you get?

Homework Helper
This problem is rigged to simplify VERY nicely Let x2=u and you should see it more easily.

Sidthewall
x^2 + 2x + 1

Sidthewall
ohhh hmm

Sidthewall
ok i see it now, but if x^2 = u then dx x= du and then dx = du/x does that makes sense ?

mmmboh
You can't put du/x inside the integral, the point of the substitution is to get rid of the x's...look at x^4+2x^2+1...there is a way to simplify it similar to how you would simplify x^2+2x+1...you won't need a substitution and then the answer is easy.

Sidthewall
sorry i am dumb i got it

Homework Helper
Oh yes sorry I never meant for you to make a substitution in the classic sense of solving an integral, but to make the substitution since u2+2u+1 is easily distinguishable as (u+1)2

Homework Helper
x^2 + 2x + 1

(1 + x4 + 2x2)1/2

= [(1 + x2)2]1/2

= (1 + x2 )

Now find the integration of (1 + x2)dx