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

[golb0016]

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.

 

[Dick]

You are going to have a tough time finding an antiderivative for that. Is it actually a definite integral?

 

[golb0016]

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?

 

[Dick]

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?

 

[golb0016]

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

 

[Dick]

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

That's the idea.