Learn how to determine the paticular solution with the given condition

The video tutorial explains how to find the function H of X by integrating its derivative, H prime of X. The process involves integrating the expression 8X^3 + 5 to obtain H of X as 2X^4 + 5X + C. The tutorial then demonstrates evaluating H of 1 to solve for the constant C, resulting in the final expression H of X = 2X^4 + 5X - 3.

What mistake did the teacher acknowledge while writing down the calculations?

What is the final expression for H of X as mentioned in the text?