Answer
\[ -2(2x^3+7)^{-1/2} +C\]
Work Step by Step
In order to integrate this function, we have to use an «u» substitution.
Choose an u, derivate it:
$ u=2x^3+7$
$ du = 6x^2dx$
Then substitute:
\[ =\int \dfrac{du}{u^{3/2}} = \int u^{-3/2}du \]
Then integrate
\[ =-2u^{-1/2} +C \]
And undo the substitution:
\[ =\boxed{-2(2x^3+7)^{-1/2} +C}\]
