Question $1$: $66$ Marks

Evaluate the following integrals:

$(1\mathrm{.}1)$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{2}{\sqrt[\phantom{2}]{4-x^2}}dx$

$(1\mathrm{.}2)$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{1}{x^2\sqrt[\phantom{2}]{4-x^2}}dx$

$(1\mathrm{.}3)$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{1}{4-9x^2}dx$

$(1\mathrm{.}4)$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{1}{-2x-x^2}dx$

$(1\mathrm{.}5)$

${\displaystyle \underset{1}{\overset{2}{}}}\frac{x^{2}3}{x^{3}2x}dx$

$(1\mathrm{.}6){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{8}{x(lnx1{)}^{\frac{3}{2}}}dx$

$(1\mathrm{.}7){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{e^{\sqrt[\phantom{2}]{x}}}{\sqrt[\phantom{2}]{x}}dx$

$(1\mathrm{.}8)$

${\displaystyle \underset{0}{\overset{\sqrt[\phantom{2}]{\frac{}{4}}}{}}}(sin2x^2{)}^{2}xcos2x^{2}dx$

$(1\mathrm{.}9){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{3(e^2{)}^2}{(e^x{)}^2{e}^x-2}dx,x>0$