$\displaystyle \int \dfrac{7}{t^{3} + 5} dt$

$\displaystyle \int 7(t^{3} + 5}^{-1} dt$

$\displaystyle u = (t^{3} + 5)$

$\displaystyle du = 3t^{2}$

$\displaystyle \dfrac{7}{3t^{2}}du = 7 dt$

$\displaystyle \dfrac{7}{3t^{2}} \int u^{-1}$

$\displaystyle \dfrac{7}{3t^{2}} \dfrac{u^{0}}{0} + C$

$\displaystyle \dfrac{7}{3t^{2}} \ln|t^{3} + 5| + C$ Right?