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

## 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.

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Dick
Homework Helper

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

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
Homework Helper

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?

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

Dick