Evaluate: \(I=80{\int }_{0}^{\frac{\pi }{2}}\frac{\sin x+\cos x}{9\sin x+16\cos x}dx\)

\(\frac{80}{327}\left[\frac{25\pi }{2}+7\ln \left(\frac{9}{16}\right)\right]\)

\(\frac{80}{337}\left[\frac{25\pi }{2}-7\ln \left(\frac{9}{16}\right)\right]\)

\(\frac{40}{327}\left[\frac{25\pi }{2}+7\ln \left(\frac{9}{16}\right)\right]\)

\(\frac{40}{327}\left[\frac{25\pi }{2}-7\ln \left(\frac{9}{16}\right)\right]\)