Evaluate the integral

Let's rewrite the integrand by completing the square for ,

Now apply integral substitution,

Let u=x+1,

Now again apply the integral substitution,

Let u=sec(v),

Now use the identity: 

assuming 

Using the identity: 

Apply the sum rule,

Now let's evaluate the first integral by applying the integral reduction,

Now use the common integral: 

Now plug back the above integral and the common integral,

 

Now substitute back: 

Now