Evaluate

We can write above integral as

Considering first integral:

Since the numerator and denominator are exactly same, our integrand simplifies to 1 and integrand becomes:

⇒ ∫ dx

⇒ x

--- (3)

Considering second integral:

Let u = 1 + e^x, du = e^xdx

Apply u – substitution:

Replacing the value of u we get,

---(4)

From (3) and (4) we get,