# Math Help - Integral Indefine

1. ## Integral Indefine

$\int{x(2-x^2)^3}\,dx$

How could I get the -1/2???

2. Originally Posted by dianjoey
$\int{x(2-x^2)^3}\,dx$

How could I get the -1/2???
I think what you want is
$
\int x(2-x^2)^3\,dx = -\frac{1}{2}\int (2-x^2)^3\, d(2-x^2)
$

but it's really better if you use a substitution. Let $u = 2-x^2$ (the hard part of this). Then $du = -2 x \,dx$ so $x\,dx = -\frac{1}{2}\,du$ so the original problem becomes

$
-\frac{1}{2} \int u^3\,du
$

3. Hi Danny,

I was asking where the $-\frac 12\$ come from...
I don't know how to get that...