Find the integral x^3 sqrt(x^2 + x^8 + 8) cos x dx

  • Thread starter golb0016
  • Start date
  • #1
golb0016
16
0

Homework Statement


Find the integral

f(x) = x^3 sqrt(x^2 + x^8 + 8) cox(x) dx


The Attempt at a Solution



I need help starting. It appears to be either integration by parts and/or substituion.
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,263
621


You are going to have a tough time finding an antiderivative for that. Is it actually a definite integral?
 
  • #3
golb0016
16
0


The problem wanted the function evaluated from -14 to 14. Does it make a difference if it is definitive or not? Is there a trick if it is definitive?
 
  • #4
Dick
Science Advisor
Homework Helper
26,263
621


The problem wanted the function evaluated from -14 to 14. Does it make a difference if it is definitive or not? Is there a trick if it is definitive?

It does in this case. For your function f(-x)=(-f(x)), it's an odd function. What happens if you integrate an odd function over a symmetric interval around the origin?
 
  • #5
golb0016
16
0


Does the positive and negative parts cancel out if it is symmetric?
 
  • #6
Dick
Science Advisor
Homework Helper
26,263
621


Does the positive and negative parts cancel out if it is symmetric?

That's the idea.
 

Suggested for: Find the integral x^3 sqrt(x^2 + x^8 + 8) cos x dx

  • Last Post
Replies
9
Views
301
  • Last Post
Replies
5
Views
340
Replies
7
Views
471
  • Last Post
Replies
6
Views
470
Replies
5
Views
493
  • Last Post
2
Replies
54
Views
3K
Replies
29
Views
809
Replies
7
Views
678
Replies
44
Views
2K
Replies
3
Views
243
Top