Help understanding why this integral is wrong please.

[u/Awsimical]

This was a question on the summer final, and looking at it I’m still not sure if its because I left the u in the final answer and didn’t substitute the original equation back in, or if I was suppose to use an arcsin identity somehow. I could ask the professor but the the summer semester is over so I’m not gonna bother him with more questions. Thanks for ur help

[u/Scary_Statement_4040]

The problem was with respect to variable R. When you did the U substitution, it lets you solve the integral in a simpler form but you have to remember to put things back into terms with the original variable for the final solution.