Integrate the given function. \( \int_{0}^{\pi / 6} x \sec x \tan x d x \) \( \int_{0}^{\pi / 6} x \sec x \tan x d x=\square \) (Round to four decimal places as needed.)

11 Calcule les limites suivantes: a) \( \lim _{x \rightarrow 0} \ln \left(\frac{x+1}{x}\right) \); b) \( \lim _{x \rightarrow 1} \frac{\ln x}{1-x^{2}} \); c) \( \lim _{x \rightarrow 0} \sqrt{x} \ln x \)

\( \left. \begin{array} { l } { \lim _ { x \rightarrow 0 } ( \frac { \sin x } { x } ) } \\ { \left. \begin{array} { l | l | l | } \hline & { - 0.001 } & { 0 } \\ { F ( x ) } & { 0.001 } \\ \hline \end{array} \right. } \end{array} \right. \)

\( \left. \begin{array} { l } { \lim _ { x \rightarrow 0 } ( \frac { \sin x } { x } ) } \\ { \left. \begin{array} { l | l | l | l | } { x } & { - 0.001 } & { 0 } & { 0.001 } \\ \hline f ( x ) & { } & { } & { } \\ \hline \end{array} \right. } \end{array} \right. \)

\( \left. \begin{array} { l } { \lim _ { x \rightarrow 0 } ( \frac { \sin x } { x } ) } \\ { \left. \begin{array} { l | l | l | l } { x } & { - 0.001 } & { 0 } & { 0.0011 } \\ \hline f ( x ) & { } & { } & { } \\ \hline \end{array} \right. } \end{array} \right. \)

\( \int _ { - 2 } ^ { 2 } ( x ^ { 3 } \cos \frac { x } { 2 } + \frac { 1 } { 2 } ) \sqrt { 4 - x ^ { 2 } } d x \)