• Support PF! Buy your school textbooks, materials and every day products Here!

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

  • Thread starter Sidthewall
  • Start date
  • #1
33
0

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
 

Answers and Replies

  • #2
ACG
46
0
Here's a bit of a hint. When you expand (x+1)^2, what do you get?
 
  • #3
Mentallic
Homework Helper
3,798
94
This problem is rigged to simplify VERY nicely :smile:

Let x2=u and you should see it more easily.
 
  • #5
33
0
ohhh hmm
 
  • #6
33
0
ok i see it now, but if x^2 = u then dx x= du and then dx = du/x does that makes sense ?
 
  • #7
407
0
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.
 
  • #8
33
0
sorry i am dumb i got it
 
  • #9
Mentallic
Homework Helper
3,798
94
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
 
  • #10
rl.bhat
Homework Helper
4,433
7
x^2 + 2x + 1
(1 + x4 + 2x2)1/2

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

= (1 + x2 )

Now find the integration of (1 + x2)dx
 

Related Threads on Integral of sqrt(1 + x^4+ 2x^2)

Replies
4
Views
2K
  • Last Post
Replies
6
Views
53K
Replies
2
Views
2K
Replies
3
Views
12K
Replies
7
Views
2K
  • Last Post
Replies
6
Views
8K
Replies
6
Views
1K
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
4
Views
65K
Top