QUESTION $5$

Evaluate the following integrals:

$($a$)$

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

$($b$)$

$(8)$

${\displaystyle \underset{0}{\overset{1}{}}}si{n}^{-1}xdx$

where $si{n}^{-1}$ is the arcsin function.

$($c$)$

$(7)$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}xta{n}^{-1}xdx$

where $ta{n}^{-1}$ is the arctan function.

$[21]$