When does integration by parts fail

[BritneyKeough]

I've spent over an hour trying to figure this out and I still don't get why integration by parts fails here. This is the solution to the indefinite integral of arcsin(x):

Now what I've been trying to figure out is why I can't use integration by parts instead of substitution for the second step?
When I try integration by parts with u=x and dv=dx/sqrt(1-x^2) I get the final integral to be 0 = 0 and it's driving me nuts. Can anyon shed some light on this please?

 

[stapel]

....why I can't use integration by parts instead of substitution for the second step?
When I try integration by parts with u=x and dv=dx/sqrt(1-x^2) I get the final integral to be 0 = 0....

Please reply showing your steps, so we can see how you're arriving at that result. Thank you!

 

[Deleted member 4993]

I've spent over an hour trying to figure this out and I still don't get why integration by parts fails here. This is the solution to the indefinite integral of arcsin(x):
View attachment 4718
Now what I've been trying to figure out is why I can't use integration by parts instead of substitution for the second step?
When I try integration by parts with u=x and dv=dx/sqrt(1-x^2) I get the final integral to be 0 = 0 and it's driving me nuts. Can anyon shed some light on this please?

What are you getting for v [by integrating dx/sqrt(1-x^2)]?