question_answer

\[\int{\frac{{{\cos }^{4}}x}{{{\sin }^{3}}x{{({{\sin }^{5}}x+{{\cos }^{5}}x)}^{3/5}}}}\,\,dx\] is equal to_______.

A)  \[\frac{-1}{5}\,\,{{\left( \frac{{{\tan }^{5}}x+1}{{{\tan }^{5}}x} \right)}^{2/5}}+C\]

B)  \[\frac{-1}{2}\,\,\,{{\left( \frac{{{\tan }^{5}}x+1}{{{\tan }^{5}}x} \right)}^{2/5}}+C\]

C)  \[\frac{-1}{2}\,\,{{\left( \frac{{{\tan }^{3/5}}x+1}{{{\tan }^{5}}x} \right)}^{5/3}}+C\]

D)  \[\frac{-1}{5}\,\,{{\left( \frac{{{\tan }^{3/5}}x+1}{{{\tan }^{5}}x} \right)}^{5/3}}+C\]

E)  None of these