Question

$\int {\cos }^{-3/7}x{\sin }^{-11/7}xdx$ 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)

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