Question

Write a value of\[\int \cos^4 x \text{ sin x dx }\]

Answer 1

Let I= \[\int\] cos⁴ x .sin x dx

Let cos x = t
⇒​ –sin x dx = dt
⇒ sin x dx = –dt

\[\therefore I =\] - \[\int\] t⁴ dt

\[= \frac{- t^5}{5} + C\]
\[ = - \frac{\cos^5 x}{5} + C \left( \because t = \cos x \right)\]