I did this integral this way but the book didn't Convert the left side into arcsin. Am I still right?Attachment 28639Attachment 28640
No, I don't think your way works. Before your substitution, you have x in the numerator so it doesn't look like the derivative of an arcsin. After your substitution, you have in the denominator, so again it doesn't look like the derivative of an arcsin.
But the integral is easy enough to do - you just substitute and it becomes a power of w.
Actually on the left side the (x-3) gets crossed out by replacing the dx with du / [2 (x-3) ]
What you should do is let and your integral becomes . Surely you can integrate that...
Thanks - but why does it require more substituion to integrate that? I obviously see there is an easier way to do the problem - I just want to know if doing 3^2 - (u^.5)^2 is still correct (after putting it into arcsin)
I just told you that it is not, because you will be required to integrate an extra square root, which requires more substitutions!
But there is a square root in arcsin right?
What hollywood and Prove It are saying is if it were simply then we can simply integrate. But your form of requires another substitution for the square root over u. It's the inner square root that is the problem here, not the outer.
I see what you're saying - sorry!
So whatever is in between the parenthesis of (root u)^2 has to be just and only u^2
u cant be anything but u?