Therefore,
Integrating yields:
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...
Consider
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?
Thoughts appreciated?
What a title!
I've not checked your calculations, but they don't have to be. When you integrate some function f(x) over
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.
You have:
and are constants, of course. But so is and , call this .
So
An indefinite integral is really a big function that accounts for all the functions whose derivative is the integrated function!