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) \[\frac{7}{4}{{\tan }^{-4/7}}x+c\]
Correct Answer: C
Solution :
\[\int{{{\cos }^{-3/7}}}x{{\sin }^{-11/7}}x\,dx\] \[=\int{\frac{{{\sin }^{-11/7}}x}{{{\cos }^{-11/7}}x}}.{{\sec }^{2}}xdx\] \[=\int{{{\tan }^{-11/7}}}x{{\sec }^{2}}x\,dx\] Let \[\tan x=t\] \[\Rightarrow \] \[{{\sec }^{2}}xdx=dt\] \[\therefore \] \[I=\int{{{t}^{-11/7}}dt}=-\frac{7}{4}{{\tan }^{-4/7}}x+c\]
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