You have misquoted your teacher in two ways:
1) that is NOT equal to x^n so you should not write "x^n= ".
2) there is no "^x" in the first denominator.
The anti-derivative of x^n is [1/(n+1)]x^(n+1)+ C.
In Latex, that is
Click on that formula to see the code for it.
Of course, you can check if an anti-derivative is correct by differentiating it.and end up with:
1/(15/2 + 1^17/2) * x^(15/2 + 1)
I tried simplifying this to: (x^17/2) / (17/2)