What is the integral of (3 cos^5 x) dx with limits from 0 to pi/2.

Set the angle of your calculator into RAD
$\displaystyle 3 \int_0^{\pi/2} (\cos x)^5 \, dx = 8/5$

$\displaystyle 3 \int_0^{\pi/2} (\cos x)^5 \, dx = 3 \cdot \dfrac{4 \cdot 2}{5 \cdot 3 \cdot 1} \cdot 1 = \dfrac{8}{5}$

$\begin{align} \displaystyle 3 \int_0^{\pi/2} \cos^5 x \, dx & = 3 \int_0^{\pi/2} \cos x (\cos^2 x)^2 \, dx \\ & = 3 \int_0^{\pi/2} \cos x (1 - \sin^2 x)^2 \, dx \\ & = 3 \int_0^{\pi/2} \cos x (1 - 2 \sin^2 x + \sin^4 x) \, dx \\ & = 3 \left[ \sin x - \dfrac{2 \sin^3 x}{3} + \dfrac{\sin^5 x}{5} \right]_0^{\pi/2} \\ & = 3 \left[ \sin (\pi/2) - \dfrac{2 \sin^3 (\pi/2)}{3} + \dfrac{\sin^5 (\pi/2)}{5} \right] - 3 \left[ 0 \right] \\ & = 3 \left[ 1 - \dfrac{2(1^3)}{3} + \dfrac{1^5}{5} \right] \\ & = \dfrac{8}{5} \end{align}$