Evaluate the integral \(\mathop \smallint \nolimits_0^{\frac{{\rm{\pi }}}{2}} \frac{{\left( {3\sin {\rm{x}} + 4\cos {\rm{x}}} \right)}}{{\sin {\rm{x}} + \cos {\rm{x}}}}{\rm{dx}}\)
1
\( \frac{{{\rm{\pi }}}}{4}\)
2
\( \frac{{7{\rm{\pi }}}}{2}\)
3
\( \frac{{7{\rm{\pi }}}}{4}\)
4
\( \frac{{7{\rm{\pi }}}}{5}\)