9. For any natural number m , evaluate

$$\int \left( x ^ { 3 m } + x ^ { 2 m } + x ^ { m } \right) \left( 2 x ^ { 2 m } + 3 x ^ { m } + 6 \right) ^ { \frac { 1 } { m } } d x , x > 0$$

\begin{enumerate}
  \setcounter{enumi}{9}
  \item Let
\end{enumerate}

$$\begin{aligned}
& \text { Let } f ( x ) = \left\{ \begin{array} { c l } 
x + a , & x < 0 \\
| x - 1 | , & x \geq 0 ,
\end{array} \right. \\
& \text { And } g ( x ) = \left\{ \begin{array} { c l } 
x + 1 & \text { if } x < 0 \\
( x - 1 ) ^ { 2 } + b & \text { if } x \geq 0
\end{array} \right.
\end{aligned}$$

where a and b aneegetive real numbers. Determine the composite function gof. (If (gof) (x) is continuous for all real x , determine the values of a and b . Further, for these values of a and b , is gof differentiable at $\mathrm { x } = 0$ ? Justify your answer.