$4\mathrm{.}1$ Determine the following integrals:

$4\mathrm{.}1\mathrm{.}1{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(x^3+5{)}^{2}dx$

$4\mathrm{.}1\mathrm{.}2{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(x^3+5{)}^5{x}^{2}dx$

$4\mathrm{.}1\mathrm{.}3{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{(lnx{)}^4}{x}dx$

$4\mathrm{.}1\mathrm{.}4{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}co{s}^{3}x*sinxdx$