I just want to know if my final answer is correct since I don't have the solution for it.
I obtained:
Also, I need some help figuring out this integral:
It is continuous from 0 to 1.
No, the first is not correct.
Divide everything by to turn the integral into
.
For the second, you need to use a substitution.
Let so that .
So your integral becomes
.
Alternatively, you could expand everything, but the expansion of is difficult unless you know the Binomial Theorem.