For example...
\(f(x)=4x^2\) The original function.
\(f'(x)=8x\) When you differentiate.
\(f(x)=4x^2+C\) When you integrate back.
Okay so in this example as expected if you diff then integrate the final result is just as the original because you do the opposite of the opposite canceling everything you have done. Fair, Fine.
But then... just-just look!
\(f(y)=17y^3-12y^4\) The original function.
Now instead of differentiating then integrating on the page for you all to see I want you to do the work as well NOT under the influence of my work to make sure it's just not me and my work who sees and get that when you integrate back you DON'T get the original function. Why ._.
If it is, in fact, the original function then simplify (with steps) for me to see :D
Thx
+37084 OK......got your ORIGINAL funcion.......when you differentiate constants go away.... when you INTEGRATE constants get added...are you differnetiatin w respect to x or y?
dx or dy ?
+118653 huh?
\(f(y)=17y^3-12y^4\\ f'(y)=51y^2-48y^3\\~\\ \int51y^2-48y^3\;dy=17y^3-12y^4+c\\~\\ as\;\; expected.\)
+118653 Perhaps you should show us your working so that we can see what you mean. 
I know what I did wrong 
I was writing math down in a document (diffing and integrating) then pasting the result & original function in a calculator if I had trouble simplifying. Silly me kept thinking that f prime of x is what I got after integrating back because I never actually finished the cycle, pasted f prime of x next to the original problem ...
(with an equal sign in between and less syntax denoting them) and they did not make a true statement. I kinda got panicky cause my problem most of the time is copying the problem down wrong and not - not finishing the problem - and I had it copied just as it should have been to begin.
So with that, I am sorry for jumping so quickly for help from anyone willing to do so!
- That guy who is probably gonna keep doing it, even though he is sorry, as he has panicky math issues.
On a side note, why do you use ∫ syntax when integrating... and it's not necessary to? So much easier to just rewrite the original alone instead of a ton of unnecessary information and gaps. Just curious if you think ∫ looks cool or like that sense of completeness... Looking at you Melody.
