Question

$ \int{{{\cos }^{-3/7}}x{{\sin }^{-11/7}}}x\,dx $ is equal to:

• A. $ \log |{{\sin }^{4/7}}x|+c $
• B. $ \frac{4}{7}{{\tan }^{4/7}}x+c $
• C. $ \frac{-7}{4}{{\tan }^{-4/7}}x+c $
• D. $ \log |{{\cos }^{3/7}}x|+c $
• E. $ \frac{7}{4}{{\tan }^{-4/7}}x+c $

Answer 1

Answer: (C)

$ \int{{{\cos }^{-3/7}}}x{{\sin }^{-11/7}}x\,dx $
$ =\int{\frac{{{\sin }^{-11/7}}x}{{{\cos }^{-11/7}}x}}.{{\sec }^{2}}xdx $
$ =\int{{{\tan }^{-11/7}}}x{{\sec }^{2}}x\,dx $
Let $ \tan x=t $ $ \Rightarrow $
$ {{\sec }^{2}}xdx=dt $
$ \therefore $ $ I=\int{{{t}^{-11/7}}dt} $
$ =-\frac{7}{4}{{\tan }^{-4/7}}x+c $