Tính tích phân của:\[{\rm{I}} = \smallint \frac{{{{\rm{e}}^{\rm{x}}}{\rm{dx}}}}{{{\rm{2 + }}{{\rm{e}}^{\rm{x}}}}}{\rm{dx}}\]

A. \[\sqrt 3 + \frac{{\rm{\pi }}}{{\rm{6}}}\]

B. \[\sqrt 3 - \frac{{\rm{\pi }}}{{\rm{6}}}\]

C. \[\frac{{{\rm{5\pi }}}}{{\rm{6}}} - \sqrt 3 \]

D. \[{\rm{\pi }} - 2\]

A. \[{\rm{I}} = 60\frac{2}{7}\]

B. \[{\rm{I}} = 66\frac{2}{7}\]

C. \[{\rm{I}} = - 60\frac{2}{7}\]

D. \[{\rm{I}} = - 66\frac{2}{7}\]

A. \[\frac{{{\rm{xsin(}}\sqrt {{\rm{1 + }}{{\rm{x}}^{\rm{2}}}} {\rm{)}}}}{{{\rm{(}}\sqrt {{\rm{1 + }}{{\rm{x}}^{\rm{2}}}} {\rm{)}}}}\]

B. \[\frac{{ - {\rm{x}}\sin (\sqrt {1 + {{\rm{x}}^2}} )}}{{(\sqrt {1 + {{\rm{x}}^2}} )}}\]

C. \[\frac{{{\rm{2xsin(}}\sqrt {{\rm{1 + }}{{\rm{x}}^{\rm{2}}}} {\rm{)}}}}{{{\rm{(}}\sqrt {{\rm{1 + }}{{\rm{x}}^{\rm{2}}}} {\rm{)}}}}\]

D. \[\frac{{{\rm{xcos(}}\sqrt {{\rm{1 + }}{{\rm{x}}^{\rm{2}}}} {\rm{)}}}}{{{\rm{(}}\sqrt {{\rm{1 + }}{{\rm{x}}^{\rm{2}}}} {\rm{)}}}}\]

A. \(\left\{ {\begin{array}{*{20}{c}}{a = - \frac{1}{4}}\\{b = \frac{{13}}{4}}\end{array}} \right.\)

B. \(\left\{ {\begin{array}{*{20}{c}}{a = - \frac{1}{4}}\\{b = - \frac{{13}}{4}}\end{array}} \right.\)

C. \(\left\{ {\begin{array}{*{20}{c}}{a = - \frac{1}{4}}\\{b = - \frac{3}{4}}\end{array}} \right.\)

D. \(\left\{ {\begin{array}{*{20}{c}}{a = \frac{1}{4}}\\{b = - \frac{3}{4}}\end{array}} \right.\)

A. \[[ - 1; + \infty )\]

B. \[(1; + \infty )\]

C. \[[\frac{{ - 1}}{3}; + \infty )\]

D. \[( - 1; + \infty )\]

A. \[{\rm{I}} = \frac{{{\rm{2\pi }}}}{{\rm{3}}} - \frac{{\sqrt 3 }}{2}\]

B. \[{\rm{I}} = \frac{{{\rm{2\pi }}}}{{\rm{3}}} + \frac{{\sqrt 3 }}{2}\]

C. \[{\rm{I}} = - \frac{{{\rm{2\pi }}}}{{\rm{3}}} - \frac{{\sqrt 3 }}{2}\]

D. \[{\rm{I}} = - \frac{{{\rm{2\pi }}}}{{\rm{3}}} + \frac{{\sqrt 3 }}{2}\]

A. p = 1, q = 3

B. p = 3, q = 1

C. p = 2, q = 2

D. p = 1, q = 2