Answer
$\dfrac{2}{3}(\sqrt{10}-\sqrt{8})$
Work Step by Step
In order to integrate this function, we have to use an «u» substitution.
Choose an u, derivate it:
$ u =x^3+9$
$ du=3x^2dx$
$ \dfrac{1}{3}du =x^2dx$
Change limits:
$x_1 = -1$
$u_1= (-1)^3+9=8$
$x_2 = 1$
$u_2=(1)^3+9=10$
Then substitute:
\[ \dfrac{1}{3} \int_{8}^{10} u^{-1/2} du \]
Then integrate
\[ \dfrac{1}{3} \bigg [ \dfrac{u^{1/2}}{1/2} \bigg ]_{8}^{10} \]
Apply calculus 2nd theorem and reduce:
\[ \dfrac{2}{3} (\sqrt{10}-\sqrt{8}) \]
