Evaluate the following integrals:

$(1\mathrm{.}1)$

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

$(1\mathrm{.}2)$

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

$(1\mathrm{.}3)$

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

$(1\mathrm{.}4)$

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

$(1\mathrm{.}5)$

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

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

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

$(1\mathrm{.}8)$

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

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

$33$

$(1\mathrm{.}10)$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x+1}{\sqrt[\phantom{2}]{3-2x-x^2}}dx$

$(1\mathrm{.}11)$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{9}{(1-3x{)}^4}dx$

$(1\mathrm{.}12)$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}se{c}^2(4)d$

$(1\mathrm{.}13)$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}3e^{-4x}dx$

Question $2$: $10$ Marks

Use $z-$substitution to integrate

$(2\mathrm{.}1){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{cosx}{1-cosx}dx$