I would do the substitution and the integral becomes
I'm supposed to solve this using an integral table and substitution.
I attempted to solve by rewriting the denominator as Sqrt((8x)^{2}+9^{2}) then using to solve, substituting u=8x.
Thereby getting the answer ln|8x+sqrt((8x)^{2}+9^{2})|+C however this is apparently not correct. Any help?
*Edit: My provided integral table can be found here
Note that Prove It's answer in log form (Inverse hyperbolic function - Wikipedia, the free encyclopedia) is exactly an eighth of yours after removing the constants.
All you missed was to divide your answer by 8 to adjust for the multiplying by eight caused by the chain rule 'on the way down', i.e. for differentiation.
The conventional way, of course, is to substitute 1/8 du for dx.
But, just in case a picture helps...
... where (key in spoiler) ...
Spoiler:
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Don't integrate - balloontegrate!
Balloon Calculus; standard integrals, derivatives and methods
Balloon Calculus Drawing with LaTeX and Asymptote!