Wanting to check my work using the subsitution method.

You have demonstrated only the ability to copy an answer. What substitution did you use?
 
I do not see any work, but the answer looks correct.

By the way, your parentheses around the sine output are unnecessary. 8-)
 
Often with substitution, look at what is in parentheses. Use that for the sub.

In this case, try letting \(\displaystyle u=x^{9}+9, \;\ \frac{du}{9}=x^{8}dx\)

This is certainly not always the case, but with this one it looks promising.

After making this sub, there is one more obvious sub you can make and you have it.
 
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