搜搜做题作业网微积分：用不定积分法解决如下不定积分
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微积分：用不定积分法解决如下不定积分
RT
RT
∫ x•cosx/sin³x dx
= ∫ xcotxcsc²x dx
= -∫ xcotx d(cotx)
= (-1/2)∫ x d(cot²x)
= (-1/2)xcot²x + (1/2)∫ cot²x dx,分部积分法
= (-1/2)xcot²x + (1/2)∫ (csc²x - 1) dx
= (-1/2)xcot²x + (1/2)(-cotx - x) + C
= (-1/2)xcot²x - (1/2)cotx - (1/2)x + C
= ∫ xcotxcsc²x dx
= -∫ xcotx d(cotx)
= (-1/2)∫ x d(cot²x)
= (-1/2)xcot²x + (1/2)∫ cot²x dx,分部积分法
= (-1/2)xcot²x + (1/2)∫ (csc²x - 1) dx
= (-1/2)xcot²x + (1/2)(-cotx - x) + C
= (-1/2)xcot²x - (1/2)cotx - (1/2)x + C