问题标题:
积分SIN^-4(X/2)
更新时间:2024-04-26 15:03:55
问题描述:
积分SIN^-4(X/2)
齐亚莉回答:
∫{[sin(x/2)]^(-4)}dx
=∫{1/[sin(x/2)]^4}dx
=-∫{1/[sin(x/2)]^2}{-1/[sin(x/2)]^2}dx
=-∫{1+[cot(x/2)]^2}d[cot(x/2)]
=-∫d[cot(x/2)]-∫{[cot(x/2)]^2}d[cot(x/2)]
=-cot(x/2)-(1/3)[cot(x/2)]^3+C.
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