Indefinite Integrals

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Step 1: Find breakpoints where expressions change sign: Step 2: - For : not needed.
- For :
So, - For :
So, Therefore, Final Answer: 3

Step 1: Use the substitution for definite integrals: Let’s check: But: So, So: Add: So, Combine numerator: So, Step 2: Substitute . So, So, Step 3: Expand denominator: So, Complete square: So, Step 4: Use formula: . Put : Therefore, Final Answer:

To solve this definite integral, we first find the indefinite integral: Here, , so: Now, apply the limits: Calculate the cosine values: So, Therefore, the answer is }.