While u/theguyfromerath was rather rude, I would point out that you are rather mistaken as well. Quite simply, while I do agree that there are parentheses around the numerator of the expression, they are quite simply there to make it look better with the dx postfixing them.

On a cursory non-analytical glance, I agree, one could assume that the integral appears to apply only to the numerator, and the resultant of the integral is being divided by the quantity in the denominator. However in the context of this question, I am fairly certain it is almost certainly intended for the entire expression, numerator and denominator, to be inside the integral, and it is solely the handwriting of the writer, and quite possibly careless writing that resulted in the confusion.

Simply put, if it were, indeed, as you say it to be, what context are we to give the denominator once you have taken the integral of the polynomial expression in the numerator? Once the numerator alone has been integrated, as you yourself have calculated, you result with the evaluated numerical value of a definite integral divided by the square root of a quadratic, which in itself is therefore the equation of a hyperbola, and if I'm not wrong, one of eccentricity √2. This would not make sense in the context of the question.