Definite Integrals

Step 1: Factor the denominator and set up the partial fraction decomposition. Multiplying by the denominator gives .
Step 2: Solve for A and B.
If , then .
If , then .
Step 3: Rewrite the integral with the partial fractions. Step 4: Integrate and evaluate the definite integral.

Step 1: Let . Use the property . Here, , so .
Step 2: Apply the property by replacing with . Step 3: Add the original and transformed integrals. Step 4: Evaluate the simple integral.