2 Attachment(s)

Integral using table and substiution (simple pics provided)

Attachment 26671I'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 Attachment 26672 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

Re: Integral using table and substiution (simple pics provided)

I would do the substitution and the integral becomes

Re: Integral using table and substiution (simple pics provided)

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...

http://www.ballooncalculus.org/draw/.../thirtytwo.png

... where (key in spoiler) ...

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