Hi guys I'm trying to work through some problems getting ready for an exam and I came across this problem that doesn't make sense to me...
If I integrate this I get
It says if we substitute x = sinh(u) we get
Where on earth does that cosh^3 come from? I know that gives us
Also if I integrate this I get I get . Why are they not equal?
What a title!
an indefinite interval, infinite number of functions that satisfy what you get (but there might be exceptions
to this) -- what you find is the set of all anti-derivatives. That's why we have the constant of integration.
and are constants, of course. But so is and , call this .
An indefinite integral is really a big function that accounts for all the functions whose derivative is the integrated function!