Question

\[\int \sin^5\text{ x }\text{cos x dx}\]

Answer 1

\[\int \sin^5 x \text{cos x dx}\]
\[Let \sin x = t\]
\[ \Rightarrow \cos x = \frac{dt}{dx}\]
\[ \Rightarrow \text{cos x dx }= dt\]
\[Now, \int \sin^5\text{ x }\text{cos x dx}\]
\[ = \int t^5 dt\]
\[ = \frac{t^6}{6} + C\]
\[ = \frac{1}{6} \sin^6 x + C\]