Question

what is the integral x(2+x)^0.5

Answer 1

shouldnt it be done by integrating by parts?

Answer 2

try substitution \(2+x = u^2\)

Answer 3

woah :O

Answer 4

my bad lol

Answer 5

You can also try \(t=2+x\), so that \(x=t-2\) and \(dx=dt\).
\[\int x\sqrt{2+x}~dx~~\iff~~\int(t-2)\sqrt t~dt=\int \left(t^{3/2}-2t^{1/2}\right)~dt\]