Some Properties Of Definite Integrals

On adding Eqs. (i) and (ii), we get

Let the integral be: Step 1: Use the property of definite integrals: Here, So, define: Step 2: Add both expressions for : Now use the identity: But rather than simplifying further, we use a better trick: Step 3: Partial fraction the denominator: So, Multiply both sides: Let
Let So, Step 4: Rewrite integral: Split the integral: Step 5: Use symmetry again: Let’s define: Now, use the result: Apply to both terms, you’ll find the sum gives a constant times Eventually, after simplification: