Find $\int \cos ^ { 3 } ( x ) \tan ( x ) d x$
A) $\frac { 1 } { 5 } \sin ^ { 5 } x + C$
B) $\frac { 1 } { 3 } \sin ^ { 3 } x + C$
C) $\frac { 1 } { 3 } \cos ^ { 3 } x + C$
D) $- \frac { 1 } { 3 } \cos ^ { 3 } x + C$

Question

Quizplus · Accepted Answer

The integral can be solved by substitution. Let $ u = \cos(x) $, then $ du = -\sin(x) dx $. The integral becomes $-\int u^3 du$, which evaluates to $-\frac{1}{4} u^4 + C$. Substituting back $ u = \cos(x) $, we get $-\frac{1}{3} \cos^3(x) + C$.

Find ∫cos⁡3(x)tan⁡(x)dx\int \cos ^ { 3 } ( x ) \tan ( x ) d x∫cos3(x)tan(x)dx

Find $\int \cos ^ { 3 } ( x ) \tan ( x ) d x$