Find the indefinite integral of the following function. $$\int \frac { \cos x } { \sin ^ { 8 } x } d x$$
A) $- \frac { ( \sin x ) ^ { - 7 } } { 7 } + C$
B) $- \frac { ( \cos x ) ^ { - 7 } } { 7 } + C$
C) $- \frac { ( \sin x ) ^ { - 7 } } { 8 } + C$
D) $- \frac { ( \sin x ) ^ { - 8 } } { 7 } + C$
E) $- \frac { ( \cos x ) ^ { - 7 } } { 8 } + C$

Question

Quizplus · Accepted Answer

The integral $\int \frac{\cos x}{\sin^8 x} dx$ can be solved by substituting $u = \sin x$, which leads to $du = \cos x dx$. This changes the integral to $\int u^{-8} du$, which integrates to $-\frac{u^{-7}}{7} + C$, or $-\frac{(\sin x)^{-7}}{7} + C$.

Find the Indefinite Integral of the Following Function ∫cos⁡xsin⁡8xdx\int \frac { \cos x } { \sin ^ { 8 } x } d x∫sin8xcosx​dx

Find the Indefinite Integral of the Following Function $\int \frac { \cos x } { \sin ^ { 8 } x } d x$