Final answer:
Due to typos in the question, it is unclear what the exact function that needs integration is, preventing a specific solution. The answer would involve techniques like substitution or integration by parts depending upon the accurate form of the function.
Step-by-step explanation:
The student has asked to integrate a function that seems to include t raised to a power and a square root of an expression involving t. However, due to some typos in the question, it's not clear what the exact function is, nor the limits of integration if any. To integrate a function of this form generally, you would identify a substitution that simplifies the integral or apply the integration by parts method. The provided excerpts from other problems suggest various methods of integration such as integration by parts, use of dummy variables, and considering the dimensions of the integral.
It's essential to first write the expression accurately and then proceed with the method that fits the function's form. For example, if the function resembles a standard integral form, you can directly apply the corresponding integral formula. Without the correct expression, we cannot provide a specific solution to this problem.