Evaluate the following indefinite integrals. Show all work.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x^3+2x^2-3}{\sqrt[3]{x}}dx$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(2sinx-\frac{2}{x})dx$

Solve the following differential equation, using the initial condition given to find the appropriate particular solution. Show all work.

$f^{\text{'}}(t)=6t-8t^3,f(2)=3$