Evaluate the following :

We have given,

We can write it as

Now, we will use Integration by a partial fraction in the second integral,

Let

4x + 3 = A(x + 1) + B(x + 3)

Now, Put x = - 3 , because fraction B will be zero then we get

4( - 3) + 3 = A( - 3 + 1) + B( - 3 + 3)

- 12 + 3 = - 2A

And, Now put x = - 1 , then we get

4( - 1) + 3 = A( - 1 + 1) + B( - 1 + 3)

- 4 + 3 = 2B

So,

Hence. This is the solution of given integral.