Answer
$\int \frac{2x+1}{\sqrt {x+4}}dx = \frac{4\sqrt {x+4}^3}{3} - 15\sqrt {x+4} + c$
Work Step by Step
Use substitution to solve for $\int \frac{2x+1}{\sqrt {x+4}}dx$:
Let $u = \sqrt {x+4}$, and solve for $x$:
$x= u^2 -4$
Find $dx$:
$dx = 2udu$
Now substitute into the integral:
$\int \frac{2(u^2-4)+1}{u}2udu$
Simplify:
$\int{4u^2-15} du$
Integrate:
$\frac{4\sqrt {x+4}^3}{3} - 15\sqrt {x+4} + c$
Substitute back:
