Trying to figure out integral with infitnite limites

  • Thread starter z00maffect
  • Start date
  • #1

Homework Statement



[tex]\int^{\infty}_{-\infty}(1/(a^{4}+(x-x_{0})^{4}))dx[/tex]

Homework Equations





The Attempt at a Solution



i let [tex]u = (x-x_{0})^{4}[/tex]

but have no idea what to go from there
 
Last edited:

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,260
619
I would use u=(x-x0)/a and factor out the a^4. That gives you 1/(1+u^4). (1+u^4)=(u^2-sqrt(2)u+1)*(u^2+sqrt(2)u+1). Use partial fractions on that. It's not an easy integral, but it can be done.
 
  • #3
awesome thanks! got [tex]\pi*\sqrt{2}/2[/tex]
 
  • #4
Dick
Science Advisor
Homework Helper
26,260
619
awesome thanks! got [tex]\pi*\sqrt{2}/2[/tex]

Good job. Don't forget to put the 'a' factor back in again.
 
  • #5
20
0
As Dick said, firstly let [tex]
u=\frac{x-x_{0}}{a} [/tex] then [tex] du= adx [/tex] and now integral becomes

[tex]
\frac{1}{a^{5}}\int^{\infty}_{-\infty}\frac{1}{1+u^{4}}du
[/tex]
Secondly, by letting [tex] u=e^{i\theta} [/tex] and [tex] du=i*{e}^{i\theta}d\theta[/tex]
you can use "residue theorem". Yet, I forgot how can we apply here. After I remember, I'll post it
 

Related Threads on Trying to figure out integral with infitnite limites

  • Last Post
Replies
2
Views
869
Replies
8
Views
833
  • Last Post
Replies
13
Views
774
Replies
4
Views
451
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
23
Views
2K
  • Last Post
Replies
5
Views
842
Replies
1
Views
1K
Replies
8
Views
1K
Replies
1
Views
2K
Top