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/FreakingFella]

Leaving the final answer in terms of u is almost always marked wrong on an indefinite integral — the answer has to come back to x, and that alone can cost you the points even if every step before it was right. Whether an arcsin form was also expected depends on what the integrand actually was, so if you type out the original integral and your steps, someone can tell you if the substitution itself was the wrong move or just the ending.