Question $1(5$ Markah$)$

Use integration $by$ partial fraction $to$ solve

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{3x+4}{(x+3{)}^2}dx$

Question $2(5$ Markah$)$

Evaluate

${\displaystyle \underset{1}{\overset{4}{}}}\frac{1}{\sqrt[\phantom{2}]{x^2-6x+25}}dx$

Question $3(5$ Markah$)$

Evaluate the following integral

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

Question $4(5$ Markah$)$

Determine whether the following integral converges $or$ div

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