Evaluate the indefinite integral.

x$2($x$3+8)8$ dx

Step $1$

We must decide what to choose for u$.$

If

u $=$ f$($x$),$

then

du $=$ f$\text{'}($x$)$ dx$,$

and so it is helpful to look for some expression in

x$2($x$3+8)8$ dx

for which the derivative is also present, though perhaps missing a constant factor.

For example,

x$3+8$

is part of this integral, and the derivative of

x$3+8$

is

$,$ which is also present except for a constant factor.