Question

Evaluate: $\int \frac{x}{\sqrt{x+4}}dx$

Answer 1

Solution:

Let $x+4=t\Rightarrow t-4=x$

$\Rightarrow dx=dt$

$I=\int \frac{t-4}{t^{1/2}}dt$

$=\int (t^{1/2}-4t^{-1/2})dt$

$=\frac{2}{3}{t}^{3/2}-8t^{1/2}+C$

$=\frac{2}{3}(x+4{)}^{3/2}-8(x+4{)}^{1/2}+C$