Integration By Parts

Step 1: Split the integral into two parts:

Step 2: Evaluate the second integral (constant term):

Step 3: Evaluate the first integral using integration by parts: Let , Then ,

Step 4: Evaluate from 0 to 1:

Step 5: Combine results:

Conclusion: The correct answer is .

Step 1: Use integration by parts with:

Step 2: Apply the integration by parts formula:

Step 3: Simplify the remaining integral:

Step 4: Perform polynomial division on the integrand:

Step 5: Integrate term by term:

Step 6: Combine all terms:

Conclusion: The correct answer is .