求不定积分∫√x/（x^3/4+1）dx等于多少?

来源：学生作业帮编辑：搜搜考试网作业帮分类：数学作业时间：2024/07/14 14:35:29

∫√xdx/(x^(3/4)+1)
=(2/3)∫d(x^(3/2)/(x^(3/4)+1)
=(4/3)∫x^(3/4)d(x^(3/4))/(x^(3/4)+1)
=(4/3)∫d(x^(3/4)) -(4/3)∫d(x^(3/4))/(x^(3/4)+1)
=(4/3)x^(3/4)-(4/3)ln|x^(3/4)+1|+C

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