question_answer

The value of the integral \[\int{\frac{{{\cos }^{3}}x+{{\cos }^{5}}x}{{{\sin }^{2}}x+{{\sin }^{4}}x}}dx\] is:

A)  \[\sin x-6{{\tan }^{-1}}(\sin x)+c\]

B)  \[\sin x-2{{(\sin x)}^{-1}}+c\]

C)  \[\sin x-2\,\,{{(\sin \,\,x)}^{-1}}-6{{\tan }^{-1}}\,\,(\sin \,\,x)+c\]

D)  \[\sin x-2\,\,{{(\sin \,\,x)}^{-1}}+5{{\tan }^{-1}}\,\,(\sin \,\,x)+c\]

E)  None of these