A hint to get started

Split the numerator and complete the square under a radical

\displaystyle\int\dfrac{x+2}{\sqrt{1-8x-4x^2}}\,dx

[2017/RI/I/3(a)]

CJC · Review Problems · Question 13

Complete the square as 5-4(x+1)² after separating a multiple of the radicand derivative.