Consider the indefinite integral $\int x^2(7 + 10x^3)^5 dx$.
The most appropriate substitution to simplify this integral is $u =
$
Then $du =
$ $dx$ (fill in the blank with a suitable constant or function of $x$),
and so $x^2 dx = c du$, for the constant $c =
$
After making these substitutions we obtain the integral $\int f(u) du$, where $f(u) =
$
This last integral, when evaluated, is
After substituting back for $u$ we obtain the following final form of the answer:
$\int x^2 (7 + 10x^3)^5 dx =
$
