Problem $1.$ Determine the following integrals!

$($a$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x^2+x^{-3}}{3}dx$

$($b$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{e}^x+x^2+\frac{1}{x}dx$

$($c$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\sqrt[\phantom{2}]{x}+\sqrt[3]{x^4}dx$