求 $\int_{\frac{\pi}{4}}^{\frac{\pi}{2}}\csc^4 x\mathrm{d}x$
求
\[\int_{\frac{\pi}{4}}^{\frac{\pi}{2}}\csc^4 x\mathrm{d}x\]
[Hint] 将被积函数拆成 $\csc^2 x\cdot\csc^2 x$, $\csc^2 x\mathrm{d}x=-\mathrm{d}\cot x$. 然后用分部积分.
Answer
求
\[\int_{\frac{\pi}{4}}^{\frac{\pi}{2}}\csc^4 x\mathrm{d}x\]
[Hint] 将被积函数拆成 $\csc^2 x\cdot\csc^2 x$, $\csc^2 x\mathrm{d}x=-\mathrm{d}\cot x$. 然后用分部积分.