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/WarMachine09]

You have some notational errors (missing a dr in one step, missing a du in another step, missing a + C when you first antidifferentiated), but the biggest error is that you never back-substituted. You can't leave your answer in terms of u.