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

[Sidthewall]

Homework Statement

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

Homework Equations

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?

 

[Mentallic]

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

 

[Mentallic]

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

 

[rl.bhat]

x^2 + 2x + 1

(1 + x⁴ + 2x²)^1/2

= [(1 + x²)²]^1/2

= (1 + x² )

Now find the integration of (1 + x²)dx