Q. $\int_{}^{}\frac{(\sec^{2}{x - 7)}}{\sin^{7}x}\ dx$ is equal to
A) $\frac{\tan x}{\sin^{7}x} + c$
B) $\frac{\cos x}{\sin^{7}x} + c$
C) $\frac{\sin x}{\cos^{7}x} + c$
D) $\frac{\sin x}{\tan^{7}x} + c$
Explanation
(a)
Let $I = \int_{}^{}\frac{(\sec^{2}{x - 7)}}{\sin^{7}x}\ dx$
$= \int_{}^{}\frac{\sin^{7}{x\sec^{2}{x - 7\sin^{7}x}}}{\left( \sin^{7}x \right)^{2}}\ dx$
$= \int_{}^{}{\frac{d}{dx}\left( \frac{\tan x}{\sin^{7}x} \right)}dx$
$= \frac{\tan x}{\sin^{7}x} + c$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.