Q. $\int_{}^{}{\cos^{- 3/7}{x\sin^{- 11/7}x}}dx$ is equal to
A) $\log{\left| \sin^{4/7}x \right| + c}$
B) $\frac{4}{7}\tan^{4/7}{x + c}$
C) $- \frac{7}{4}\tan^{- 4/7}{x + c}$
D) $\log{\left| \cos^{3/7}x \right| + c}$
Explanation
(c)
$\int_{}^{}{\cos^{- 3/7}{x\sin^{- 11/7}x}}dx = \int_{}^{}\frac{\sin^{- 11/7}x}{\cos^{- 11/7}x}.\sec^{2}xdx$
$= \int_{}^{}{\tan^{- 11/7}x\sec^{2}x}dx$
Put $\tan x = t\ \Rightarrow \ \ \sec^{2}xdx = dt$
$\therefore\ I = \int_{}^{}t^{- 11/7}dt = - \frac{7}{4}\tan^{- 4/7}x + c\$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.