$\int x \sqrt{x+2} d x$ is equal to :
Answer & explanation
Correct answer: option 1
$\int x \sqrt{x+2} d x$
so y = x + 2 ⇒ dy = dx
y - 2 = x
⇒ $I = \int (y - 2) \sqrt{y} dy = \frac{2}{5} y^{\frac{5}{2}}-\frac{4}{3} y^{\frac{3}{2}}+ C$
$=\frac{2}{5}(x+2)^{\frac{5}{2}}-\frac{4}{3}(x+2)^{\frac{3}{2}}+C$
Option: 1