MHB 2.6.62 inverse integrals with substitution

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The discussion centers on the use of custom macros in an Overleaf document related to inverse integrals and substitution. The original poster expresses uncertainty about the correct application of variables b, x, and u in their work. A participant points out a specific error in the solution where the differential was incorrectly stated as du=dx instead of the correct form, du/4=dx. The conversation highlights the importance of careful substitution in integral calculus. Overall, the thread emphasizes the need for clarity and accuracy in mathematical notation.
karush
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ok this is from my overleaf doc
so too many custorm macros to just paste in code
but I think its ok,,, not sure about all details.
appreciate comments...

I got ? somewhat on b and x and u being used in the right places
 

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karush said:
ok this is from my overleaf doc
so too many custorm macros to just paste in code
but I think its ok,,, not sure about all details.
appreciate comments...

I got ? somewhat on b and x and u being used in the right places
Ummm...

What exactly is your question?

-Dan
 
OK this one was kinda obvious but usually that is where I make the errors especially where there is substitution.
I post another one here soon.:cool:
 
karush said:
View attachment 9267
That all looks correct to me, except that at one point in the solution of 6.6.62 you have written $du=dx$. That should be $\dfrac{du}4 = dx$ (which is what you have correctly used in the following line).
 

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