코사인 세제곱 적분

$\displaystyle \int _{0} ^{\frac{\pi}{2}} \cos x dx + 3 \int _{0} ^{\frac{\pi}{2}} \cos ^{3} x dx$ $\displaystyle = \left[ \sin x \right] _{0} ^{\frac{\pi}{2}} + 3 \int _{0} ^{\frac{\pi}{2}} ( 1 - \sin ^{2} x ) \cos x dx$ $\displaystyle = 1 + 3 \int _{0} ^{1} ( 1 - t ^{2} ) dt$ ($\because \sin x = t$) $\displaystyle = 1 + 3 \left[ t - {\frac{t ^{3}}{3}} \right] _{0} ^{1}$ $= 1 + 2 = 3$