PART 5：例題-約化公式

\(n = 2,\) 

\(\int {{{\sin }^2}x\;dx}  =  - \frac{1}{2}\cos x\sin x + \frac{1}{2}\int {dx} \) \( =  - \frac{1}{2}\cos x\sin x + \frac{x}{2} + C\)

\(n = 3,\) 

\(\int {{{\sin }^3}x\;dx}  =  - \frac{1}{3}\cos x{\sin ^2}x + \frac{2}{3}\int {\sin xdx} \) 

\( =  - \frac{1}{3}\cos x{\sin ^2}x - \frac{2}{3}\cos x + C\)

\(n = 5,\) 

\(\int {{{\sin }^5}x\;dx}  =  - \frac{1}{5}\cos x{\sin ^4}x + \frac{4}{5}\int {{{\sin }^3}xdx} \) ，

再將 \(\int {{{\sin }^3}x\;dx} \) 的結果代入