Integral Calculus

Step 1: Rewrite the quadratic expression inside the square root. We can complete the square for : Thus, the integral becomes: Step 2: Use the standard trigonometric substitution . Then, , and the expression inside the square root becomes: So, the integral simplifies to: Step 3: Integrating , we get: Step 4: Substitute , yielding:

Step 1: Start by simplifying the given expression. We use the identity for to convert it into a more convenient form: Step 2: Substitute this identity into the integral: Step 3: Now, perform substitution. Let: The integral becomes: Step 4: Using standard integral techniques, the result of the integral is: