Evaluate the integral using any appropriate algebraic method or trigonometric identity.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{dx}{(x+4)\sqrt[\phantom{2}]{x^2+8x+15}}$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{dx}{(x+4)\sqrt[\phantom{2}]{x^2+8x+15}}=$

$$